eslamelidy

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1 years, 181 days

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These are replies submitted by eslamelidy

@mmcdara i don't understand you what are you mean ?

 

@eslamelidy thank you for replying but an errer appare in this worksheet asd.mw and i want the resluts in Data

@dharr this last worksheet now b in loop change i want plot the values of  b ,(abs(x(z)))^2 such that b on x-axis   and(abs(x(z)))^2 on y-axis  also b and (abs(y(z)))^2  thanks alot final3.mw

@dharr thank you for helping me very much ,another question i want to table the values of b ,x(z),,y(z),(squre modulsof x(z),squre moduls of y(z) )as clear in picture and graph the curve of (b on x-axis and squre modulus of x(z) on y-axis also the same for b and the squre moduls of y(z)) on the same graph as shown in picture above thanks alot .final.mw

@dharr this initial vaule problem ,systems depend on integrals above 

@dharr the farward woksheet is modification of this worksheet with helping somebodys final.mw

the problem is from beinng  i have system of two diff equations  but the cofficients are  integrals depend on varible z , iwant to solve the system by any numeric method calling integrals and get solutions at z=500 

@dharr  is the procdure is correct  i didn't think so . please review the proc of functions of integrals

@dharr  please can you help me i would try from 5 months to nown but i didn't ,can you evaluate it with determining step in integral or using numerical method in integrals ,i need this work very important in my work

@acer thanks for replying show that problem i want to solution of system of differential at z=500 with  attereted b=.1 ,.2,.3,.4 .....to 50   and calling integrals with upper limit equal to 500 and soltions is complex and draw the result with b (b on x-axis and moduls of  x(500)^2,y(500)^2 on y-axis  ) 
 

``

restart

with(Physics):

with(IntegrationTools):

v := 1;

1

 

-500

 

.1

 

.5

 

.5

(1)

``

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

M[2] := expand(M[1]):

NULL

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

NULL

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

NULL

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

NULL

M[6] := Int(-Physics:-`*`(Physics:-`*`(2, exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(v, exp(sqrt(b^2+t^2))))-Physics:-`*`(Physics:-`*`(2, exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(v, exp(sqrt(b^2+t^2)))), t = -500 .. z, method = _Gquad):

M[7] := Int(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, t), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(v, exp(sqrt(b^2+t^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, t), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(v, exp(sqrt(b^2+t^2)))), t = -500 .. z, method = _Gquad):

M := Physics:-`*`(z^2, M[3])+Physics:-`*`(z, M[4])+M[5]+Physics:-`*`(z, M[6])+M[7]:

``

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

Mc[2] := expand(Mc[1]):

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

NULL

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

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

Mc[6] := Int(-Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), t^2), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+t^2), v^2), exp(sqrt(b^2+t^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, I), t^2), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+t^2), v^2), exp(sqrt(b^2+t^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, t), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(v, exp(sqrt(b^2+t^2))))+Physics:-`*`(Physics:-`*`(Physics:-`*`(2, t), exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(v, exp(sqrt(b^2+t^2)))), t = -500 .. z, method = _Gquad):

Mc := Mc[3]+Mc[4]+Mc[5]+Mc[6]:

NULL

NULL

NULL

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

N[2] := expand(N[1]):

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

N[6] := Physics:-`*`(z, Int(-Physics:-`*`(Physics:-`*`(2, exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+t^2), v), exp(sqrt(b^2+t^2))))+Physics:-`*`(Physics:-`*`(2, exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+t^2), v), exp(sqrt(b^2+t^2)))), t = -500 .. z, method = _Gquad)):

N := N[5]+N[6]:

NULL

NULL

Nc[1] := Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(2, exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(1/2, I), q-p), v), z))), exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(1/2, I), p-q), v), t))), Physics:-`*`(Physics:-`*`(z, 1/v)-Physics:-`*`(t, 1/v), exp(-sqrt(b^2+t^2)+Physics:-`*`(Physics:-`*`(Physics:-`*`(I, p), v), t))-exp(-sqrt(b^2+t^2)-Physics:-`*`(Physics:-`*`(Physics:-`*`(I, q), v), t)))-Physics:-`*`(Physics:-`*`(I, sqrt(b^2+t^2)), exp(-sqrt(b^2+t^2)-Physics:-`*`(Physics:-`*`(Physics:-`*`(I, q), v), t)))), 1/sqrt(b^2+t^2)):

Nc[2] := expand(Nc[1]):

NULL

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

NULL

Nc[6] := Physics:-`*`(z, Int(Physics:-`*`(Physics:-`*`(2., exp(Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+t^2), v), exp(sqrt(b^2+t^2))))-Physics:-`*`(Physics:-`*`(2., exp(-Physics:-`*`(Physics:-`*`(Physics:-`*`(.5, I), v), t))), 1/Physics:-`*`(Physics:-`*`(sqrt(b^2+t^2), v), exp(sqrt(b^2+t^2)))), t = -500 .. z, method = _Gquad)):

NULL

Nc := Nc[5]+Nc[6]:

NULL

 

NULL

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):

NULL

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):

NULL

eq1 := proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(-I*Mc*(-1/2+(1/2)*p^2*v^2+1/sqrt(b^2+z^2)+V)/((M*Mc-1)*v)+I*((-1/2+(1/2)*p^2*v^2+1/sqrt(b^2+z^2))*Mc+Nc)/((M*Mc-1)*v)) end proc:

eq2 := proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(-I*Mc*((-1/2+(1/2)*q^2*v^2+1/sqrt(b^2+z^2))*M+N)/((M*Mc-1)*v)+I*(-1/2+(1/2)*q^2*v^2+1/sqrt(b^2+z^2)+Vc)/((M*Mc-1)*v)) end proc;

proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(-Physics:-`*`(Physics:-`*`(Physics:-`*`(I, Mc), Physics:-`*`(-2^(-1)+((2^(-1))*q^2)*v^2+Physics:-`*`(1, Physics:-`^`(sqrt(b^2+Physics:-`^`(z, 2)), -1)), M)+N), Physics:-`^`(Physics:-`*`(M*Mc-1, v), -1))+Physics:-`*`(Physics:-`*`(I, -2^(-1)+((2^(-1))*q^2)*v^2+Physics:-`*`(1, Physics:-`^`(sqrt(b^2+Physics:-`^`(z, 2)), -1))+Vc), Physics:-`^`(Physics:-`*`(M*Mc-1, v), -1))) end proc

(2)

eq3 := 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)+V)/((M*Mc-1)*v)-I*M*((-1/2+(1/2)*p^2*v^2+1/sqrt(b^2+z^2))*Mc+Nc)/((M*Mc-1)*v)) end proc;

proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(Physics:-`*`(Physics:-`*`(I, -2^(-1)+((2^(-1))*p^2)*v^2+Physics:-`*`(1, Physics:-`^`(sqrt(b^2+Physics:-`^`(z, 2)), -1))+V), Physics:-`^`(Physics:-`*`(M*Mc-1, v), -1))-Physics:-`*`(Physics:-`*`(Physics:-`*`(I, M), Physics:-`*`(-2^(-1)+((2^(-1))*p^2)*v^2+Physics:-`*`(1, Physics:-`^`(sqrt(b^2+Physics:-`^`(z, 2)), -1)), Mc)+Nc), Physics:-`^`(Physics:-`*`(M*Mc-1, v), -1))) end proc

(3)

eq4 := 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))*M+N)/((M*Mc-1)*v)-I*M*(-1/2+(1/2)*q^2*v^2+1/sqrt(b^2+z^2)+Vc)/((M*Mc-1)*v)) end proc;

proc (z) local t; if not z::numeric then return ('procname')(args) end if; evalf(Physics:-`*`(Physics:-`*`(I, Physics:-`*`(-2^(-1)+((2^(-1))*q^2)*v^2+Physics:-`*`(1, Physics:-`^`(sqrt(b^2+Physics:-`^`(z, 2)), -1)), M)+N), Physics:-`^`(Physics:-`*`(M*Mc-1, v), -1))-Physics:-`*`(Physics:-`*`(Physics:-`*`(I, M), -2^(-1)+((2^(-1))*q^2)*v^2+Physics:-`*`(1, Physics:-`^`(sqrt(b^2+Physics:-`^`(z, 2)), -1))+Vc), Physics:-`^`(Physics:-`*`(M*Mc-1, v), -1))) end proc

(4)

``

sys := {diff(X(z), z) = Physics:-`*`(eq1, Y(z))+Physics:-`*`(eq2, X(z)), diff(Y(z), z) = Physics:-`*`(eq3, Y(z))+Physics:-`*`(eq4, X(z))}

{diff(X(z), z) = eq1*Y(z)+eq2*X(z), diff(Y(z), z) = eq3*Y(z)+eq4*X(z)}

(5)

s

s

(6)

 

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

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

(7)

``

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

Error, (in dsolve/numeric/process_input) input system must be an ODE system, found {}

 

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Download eslam.mw

@acer please  Iwant the solution complex

and i want you help me in my problem 

@brian bovril  Iwant to put z=500 but at the calculation of diff equations that calling the integrals and calculate them and substitued in diff eqs and calculate the result

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