eslamelidy

5 Reputation

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1 years, 181 days

MaplePrimes Activity


These are questions asked by eslamelidy

i want to solve the systems of diff equation what's the problem   0.mw


i want someone hlep me in this worksheet the diff eq of complex i want to sovle it with any numeric method 
 

restart

with(Physics):

with(IntegrationTools):

v := 1;

1

 

-500

 

.1

 

.5

 

.5

(1)

``

M[1] := Int(-Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2)))), tt = -500 .. z)

Int(-(2*I)*exp(-(.5*I)*tt)/((0.1e-1+tt^2)^(1/2)*exp((0.1e-1+tt^2)^(1/2)))+(2*I)*exp((.5*I)*tt)/((0.1e-1+tt^2)^(1/2)*exp((0.1e-1+tt^2)^(1/2))), tt = -500 .. z)

(2)

M[2] := Int(Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(4, I), tt), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2))))-Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(4, I), tt), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2)))), tt = -500 .. z):

M[3] := Int(-Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), tt^2), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), tt^2), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2)))), tt = -500 .. z):

M[4] := Int(-Physics:-`*`(Physics:-`*`(2, exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(v, exp(sqrt(b^2+tt^2))))-Physics:-`*`(Physics:-`*`(2, exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(v, exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, tt), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(v, exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, tt), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(v, exp(sqrt(b^2+tt^2)))), tt = -500 .. z):

M := Physics:-`*`(z^2, M[1])+Physics:-`*`(z, M[2])+Physics:-`*`(z, M[3])+M[4]:

Mc[1] := Physics:-`*`(z^2, Int(-Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2)))), tt = -500 .. z)):

Mc[2] := Physics:-`*`(z, Int(Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(4, I), tt), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2))))-Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(4, I), tt), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2)))), tt = -500 .. z)):

Mc[3] := Physics:-`*`(z, Int(-Physics:-`*`(Physics:-`*`(2, exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(v, exp(sqrt(b^2+tt^2))))-Physics:-`*`(Physics:-`*`(2, exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(v, exp(sqrt(b^2+tt^2)))), tt = -500 .. z)):

Mc[4] := Int(-Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), tt^2), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), tt^2), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v^2), exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, tt), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(v, exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, tt), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(v, exp(sqrt(b^2+tt^2)))), tt = -500 .. z):

Mc := Mc[1]+Mc[2]+Mc[3]+Mc[4]:

N[1] := Int(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, tt), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v), exp(sqrt(b^2+tt^2))))-Physics:-`*`(Physics:-`*`(Physics:-`*`(2, tt), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v), exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/exp(sqrt(b^2+tt^2))), tt = -500 .. z):

N[2] := Physics:-`*`(z, Int(-Physics:-`*`(Physics:-`*`(2, exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v), exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(2, exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v), exp(sqrt(b^2+tt^2)))), tt = -500 .. z)):

N := N[1]+N[2]:

Nc[1] := Int(-Physics:-`*`(Physics:-`*`(Physics:-`*`(2., tt), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v), exp(sqrt(b^2+tt^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2., tt), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v), exp(sqrt(b^2+tt^2))))-Physics:-`*`(Physics:-`*`(Physics:-`*`(2., I), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/exp(sqrt(b^2+tt^2))), tt = -500 .. z):

Nc[2] := Physics:-`*`(z, Int(Physics:-`*`(Physics:-`*`(2., exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v), exp(sqrt(b^2+tt^2))))-Physics:-`*`(Physics:-`*`(2., exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), tt))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+tt^2), v), exp(sqrt(b^2+tt^2)))), tt = -500 .. z)):

Nc := Nc[1]+Nc[2]:

V := Physics:-`*`(Physics:-`*`(1/Physics:-`*`(4, Pi^2), 1/sqrt(b^2+z^2)), Physics:-`*`(exp(-Physics:-`*`(2, sqrt(b^2+z^2))), Physics:-`*`(2, sqrt(b^2+z^2))+2)-2):

Vc := Physics:-`*`(Physics:-`*`(Physics:-`*`(-1, 1/Physics:-`*`(4, Pi^2)), 1/sqrt(b^2+z^2)), Physics:-`*`(exp(-Physics:-`*`(2, sqrt(b^2+z^2))), Physics:-`*`(2, sqrt(b^2+z^2))+2)-2):

``

H := proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(-I*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(-1/2+(1/2)*p^2*v^2+1/sqrt(b^2+z^2)+(1/4)*(exp(-2*sqrt(b^2+z^2))*(2*sqrt(b^2+z^2)+2)-2)/(Pi^2*sqrt(b^2+z^2)))/(((z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))-1)*v)+I*((-1/2+(1/2)*p^2*v^2+1/sqrt(b^2+z^2))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int((-1)*2.*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+2.*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+(-1)*2.*I*exp((-1)*.5*I*v*tt)/exp(sqrt(b^2+tt^2)), tt = -500 .. z)+z*(Int(2.*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+(-1)*2.*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2))), tt = -500 .. z)))/(((z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))-1)*v)) end proc:

H(500)

-6.287499768+0.1713975e-19*I

(3)

NULL

L := proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(-I*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*((-1/2+(1/2)*q^2*v^2+1/sqrt(b^2+z^2))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(2*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))-2*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+(2*I)*exp((-1)*.5*I*v*tt)/exp(sqrt(b^2+tt^2)), tt = -500 .. z)+z*(Int(-2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2))), tt = -500 .. z)))/(((z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))-1)*v)+I*(-1/2+(1/2)*q^2*v^2+1/sqrt(b^2+z^2)-(1/4)*(exp(-2*sqrt(b^2+z^2))*(2*sqrt(b^2+z^2)+2)-2)/(Pi^2*sqrt(b^2+z^2)))/(((z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))-1)*v)) end proc:

``

G := proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(I*(-1/2+(1/2)*p^2*v^2+1/sqrt(b^2+z^2)+(1/4)*(exp(-2*sqrt(b^2+z^2))*(2*sqrt(b^2+z^2)+2)-2)/(Pi^2*sqrt(b^2+z^2)))/(((z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))-1)*v)-I*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*((-1/2+(1/2)*p^2*v^2+1/sqrt(b^2+z^2))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int((-1)*2.*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+2.*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+(-1)*2.*I*exp((-1)*.5*I*v*tt)/exp(sqrt(b^2+tt^2)), tt = -500 .. z)+z*(Int(2.*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+(-1)*2.*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2))), tt = -500 .. z)))/(((z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))-1)*v)) end proc:

``

K := proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(I*((-1/2+(1/2)*q^2*v^2+1/sqrt(b^2+z^2))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(2*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))-2*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+(2*I)*exp((-1)*.5*I*v*tt)/exp(sqrt(b^2+tt^2)), tt = -500 .. z)+z*(Int(-2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2)))+2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v*exp(sqrt(b^2+tt^2))), tt = -500 .. z)))/(((z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))-1)*v)-I*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(-1/2+(1/2)*q^2*v^2+1/sqrt(b^2+z^2)-(1/4)*(exp(-2*sqrt(b^2+z^2))*(2*sqrt(b^2+z^2)+2)-2)/(Pi^2*sqrt(b^2+z^2)))/(((z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))*(z^2*(Int(-(2*I)*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int((4*I)*tt*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))-(4*I)*tt*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+z*(Int(-2*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))-2*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))+Int(-(2*I)*tt^2*exp((-1)*.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+(2*I)*tt^2*exp(.5*I*v*tt)/(sqrt(b^2+tt^2)*v^2*exp(sqrt(b^2+tt^2)))+2*tt*exp((-1)*.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2)))+2*tt*exp(.5*I*v*tt)/(v*exp(sqrt(b^2+tt^2))), tt = -500 .. z))-1)*v)) end proc:

NULL

NULL

sys := {diff(X(z), z) = Physics:-`*`(H(z), Y(z))+Physics:-`*`(L(z), X(z)), diff(Y(z), z) = Physics:-`*`(G(z), Y(z))+Physics:-`*`(K(z), X(z))}

{diff(X(z), z) = H(z)*Y(z)+L(z)*X(z), diff(Y(z), z) = G(z)*Y(z)+K(z)*X(z)}

(4)

IC_1 := {X(-500) = 0, Y(-500) = 1}

{X(-500) = 0, Y(-500) = 1}

(5)

dsol3 := dsolve(`union`(sys, IC_1), numeric, method = dverk78, output = procedurelist, known = [H, L, G, K])

proc (x_dverk78) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_dverk78) else _xout := evalf(x_dverk78) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _fcn, _i, _octl, _ctl, _y0, _yini, _ycur, _reinit, _pars, _n, _ysav, _ini, _par; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; Digits := max(15, Digits); _xout := _xin; _octl := array( 1 .. 32, [( 1 ) = (3), ( 2 ) = (1), ( 3 ) = (0), ( 4 ) = (0), ( 5 ) = (0), ( 6 ) = (0), ( 7 ) = (0), ( 9 ) = (1), ( 8 ) = (0), ( 11 ) = (-1), ( 10 ) = (-1), ( 13 ) = (-1), ( 12 ) = (-1), ( 15 ) = (-1), ( 14 ) = (-1), ( 18 ) = (-1), ( 19 ) = (-1), ( 16 ) = (-1), ( 17 ) = (-500.), ( 22 ) = (-1), ( 23 ) = (-1), ( 20 ) = (-500.), ( 21 ) = (-1), ( 27 ) = (-499.), ( 26 ) = (2), ( 25 ) = (-500.), ( 24 ) = (0), ( 31 ) = (-500.), ( 30 ) = (1), ( 29 ) = (2), ( 28 ) = (0.1e-7), ( 32 ) = (0)  ] ); _yini := Array(0..2, {(1) = -500., (2) = 0.}); _y0 := Array(0..2, {(1) = -500., (2) = 0.}); _ycur := array( 1 .. 2, [ ] ); _ctl := array( 1 .. 32, [( 1 ) = (3), ( 2 ) = (1), ( 3 ) = (0), ( 4 ) = (0), ( 5 ) = (0), ( 6 ) = (0), ( 7 ) = (0), ( 9 ) = (1), ( 8 ) = (0), ( 11 ) = (-1), ( 10 ) = (-1), ( 13 ) = (-1), ( 12 ) = (-1), ( 15 ) = (-1), ( 14 ) = (-1), ( 18 ) = (-1), ( 19 ) = (-1), ( 16 ) = (-1), ( 17 ) = (-500.), ( 22 ) = (-1), ( 23 ) = (-1), ( 20 ) = (-500.), ( 21 ) = (-1), ( 27 ) = (-499.), ( 26 ) = (2), ( 25 ) = (-500.), ( 24 ) = (0), ( 31 ) = (-500.), ( 30 ) = (1), ( 29 ) = (2), ( 28 ) = (0.1e-7), ( 32 ) = (0)  ] ); _fcn := proc (N, X, Y, YP) option `[Y[1] = X(z), Y[2] = Y(z)]`; YP[1] := H(X)*Y[2]+L(X)*Y[1]; YP[2] := G(X)*Y[2]+K(X)*Y[1]; 0 end proc; _pars := []; _n := 2; _ysav := Array(1..2, {(1) = 0., (2) = 1.}); if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then return _y0[0] elif _xout = "method" then return "dverk78" elif _xout = "numfun" then return round(_ctl[24]) elif _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _ctl[17]-_y0[0] = 0. then error "no information is available on last computed point" else _xout := _ctl[17] end if elif _xout = "enginedata" then return eval(_octl, 1) elif _xout = "function" then return eval(_fcn, 1) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _yini) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n, _ini, _yini, _pars) end if; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_par))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if; _octl[25] := _y0[0]; _octl[20] := _y0[0]; _octl[17] := _y0[0]; _octl[31] := _y0[0]; for _i to op(2, op(2, op(_octl))) do _ctl[_i] := _octl[_i] end do; for _i to _n+nops(_pars) do _ysav[_i] := _y0[_i] end do; if _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] else return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] end if else return "procname" end if end if; if _y0[0]-_xout = 0. then return [seq(_y0[_i], _i = 0 .. _n)] elif _octl[31]-_y0[0] = 0. then _octl[31] := _y0[0]-sign(_xout-_y0[0]) end if; _reinit := false; if _xin <> "last" then if 0 < 0 and `dsolve/numeric/checkglobals`(0, table( [ ] ), _pars, _n, _yini) then _reinit := true; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_par))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if end if; if _pars <> [] and select(type, {seq(_yini[_n+_i], _i = 1 .. nops(_pars))}, 'undefined') <> {} then error "parameters must be initialized before solution can be computed" end if end if; if _reinit or _ctl[17]-_xout <> 0. then if _reinit or 0 < _ctl[18] and _xout < _ctl[31] or _ctl[18] < 0 and _ctl[31] < _xout then for _i to op(2, op(2, op(_octl))) do _ctl[_i] := _octl[_i] end do; for _i to _n+nops(_pars) do _ysav[_i] := _y0[_i] end do else _ctl[29] := 2 end if; _ctl[9] := 2; _ctl[27] := _xout; if Digits <= trunc(evalhf(Digits)) then try evalhf(`dsolve/numeric/dverk78_engine`(_fcn, var(_ysav), var(_ycur), `dsolve/numeric/dverk78_aa`, `dsolve/numeric/dverk78_cc`, `dsolve/numeric/dverk78_dd`, var(_ctl), var(array( 1 .. 2, [ ] )), var(array( 1 .. 2, [ ] )), var(array( 1 .. 2, 1 .. 23, [ ] )))) catch: if searchtext('evalhf', lastexception[2]) <> 0 or searchtext('real', lastexception[2]) <> 0 or searchtext('hardware', lastexception[2]) <> 0 then `dsolve/numeric/dverk78_engine`(_fcn, _ysav, _ycur, `dsolve/numeric/dverk78_aa`, `dsolve/numeric/dverk78_cc`, `dsolve/numeric/dverk78_dd`, _ctl, array( 1 .. 2, [ ] ), array( 1 .. 2, [ ] ), array( 1 .. 2, 1 .. 23, [ ] )) else error  end if end try else `dsolve/numeric/dverk78_engine`(_fcn, _ysav, _ycur, `dsolve/numeric/dverk78_aa`, `dsolve/numeric/dverk78_cc`, `dsolve/numeric/dverk78_dd`, _ctl, array( 1 .. 2, [ ] ), array( 1 .. 2, [ ] ), array( 1 .. 2, 1 .. 23, [ ] )) end if; if _ctl[29]-3 <> 0 then Rounding := `if`(_y0[0] < _xout, -infinity, infinity); if _ctl[29]+1 = 0 then error "cannot evaluate the solution past %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_ctl[20]) elif _ctl[29]+2 = 0 then error "cannot evaluate the solution past %1, hmin > hmax, maybe error tolerance is too small", evalf[8](_ctl[20]) elif _ctl[29]+3 = 0 then error "cannot evaluate the solution past %1, step size < hmin, problem may be singular or error tolerance may be too small", evalf[8](_ctl[20]) else error "cannot evaluate the solution past %1, unknown error code returned from dverk78: %2", evalf[8](_ctl[20]), _ctl[29] end if end if; if _Env_smart_dsolve_numeric = true then if _y0[0] < _ctl[17] and procname("right") < _ctl[17] then procname("right") := _ctl[17] elif _ctl[17] < _y0[0] and _ctl[17] < procname("left") then procname("left") := _ctl[17] end if end if end if; [_ctl[25], seq(_ycur[_i], _i = 1 .. _n)] end proc, (2) = Array(0..0, {}), (3) = [z, X(z), Y(z)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_dverk78, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_dverk78, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_dverk78, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_dverk78, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_dverk78), 'string') = rhs(x_dverk78); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_dverk78), 'string') = rhs(x_dverk78)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_dverk78) else _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_dverk78) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(6)

dsol3(500)

Warning,  computation interrupted

 

NULL

NULL

``


 

Download dver.mw


 

NULL

 

Typesetting:-delayDotProduct(with, DEtools, true):

with(IntegrationTools):

z := 'z';

z

(1)

whattype(z)

symbol

(2)

``

eq := proc (z) options operator, arrow; evalf(Int(-(2*I)*exp((-1)*.5*I*t)/(sqrt(t^2+1)*exp(sqrt(t^2+1))), t = -500 .. z)) end proc

proc (z) options operator, arrow; evalf(Int(-(2*I)*exp((-1)*.5*I*t)/(sqrt(t^2+1)*exp(sqrt(t^2+1))), t = -500 .. z)) end proc

(3)

f(500)

f(500)

(4)

a := 2*t^2+5*t

2*t^2+5*t

(5)

s := t^2+t+1

t^2+t+1

(6)

d := t^2+t-9

t^2+t-9

(7)

``

 

 

sys := {diff(x(t), t) = eq(z)*y(t)+a*x(t), diff(y(t), t) = s*x(t)+d*y(t)}

{diff(x(t), t) = (Int(-(2.*I)*exp(-(.5*I)*t)/((t^2+1.)^(1/2)*exp((t^2+1.)^(1/2))), t = -500. .. z))*y(t)+(2*t^2+5*t)*x(t), diff(y(t), t) = (t^2+t+1)*x(t)+(t^2+t-9)*y(t)}

(8)

IC_1 := {x(-1) = 0, y(-1) = 1}

{x(-1) = 0, y(-1) = 1}

(9)

dsol3 := dsolve(`union`(sys, IC_1), numeric, parameters = [z], method = rkf45, range = -500 .. 500, output = procedurelist)

"dsol3:=proc(x_rkf45) ... end proc"

(10)

dsol3(parameters)

[z = undefined]

(11)

``

dsol3(parameters = [500])

Error, (in evalf/int) invalid arguments

 

dsol3(500);

Error, (in dsol3) parameters must be initialized before solution can be computed

 

``

``

``

``

``

``

``

``

``

``

``

``

``

``

``

``

``

``


 

Download eslam_().mw

general_solution.mwI want to calculate the diff equations numerical solutions at z=500 with calling the integrals with limits -500..Z and i want the datefile of resualts

 

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