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michel_h

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How do i solve below nonhomogeneous inte...

michel_h 15 Maple 2017
differential-equation integro-differential-equation
June 12 2018
1 2


 

> 

restart
> 

Digits := 4
> 

"phi(x):=16*x^(2)*(1-x)^(2):"
> 

``
> 

a1 := int((diff(phi(x), x, x, x, x))*phi(x), x = 0 .. L)

(6144/5)*L^5-3072*L^4+2048*L^3

 (1)
> 

``
> 

a3 := int(phi(x)*phi(x), x = 0 .. L)

(256/9)*L^9-128*L^8+(1536/7)*L^7-(512/3)*L^6+(256/5)*L^5

 (2)
> 

``
> 

lambda := 0.170e-1

0.170e-1

 (3)
> 

B := 0.223e11

0.223e11

 (4)
> 

A := 0.346e11

0.346e11

 (5)
> 

k[n] := W*(4*R*G*L^2+pi^2*(2*n-1)^2)/(C*(pi^2*(2*n-1)^2+4*R*L^2*(G+W)))

W*(4*R*G*L^2+pi^2*(2*n-1)^2)/(C*(pi^2*(2*n-1)^2+4*R*L^2*(G+W)))

 (6)
> 

b[n] := 4*pi*(2*n-1)/(4*R*G*L^2+pi^2*(2*n-1)^2)

4*pi*(2*n-1)/(4*R*G*L^2+pi^2*(2*n-1)^2)

 (7)
> 

U := Heaviside(t)

Heaviside(t)

 (8)
> 

w := 1

1

 (9)
> 

L := 3.5

3.5

 (10)
> 

Ra := 9

9

 (11)
> 

Rb := 5

5

 (12)
> 

W := 1

1

 (13)
> 

G := 0.5e-3

0.5e-3

 (14)
> 

R := Ra+Rb

14

 (15)
> 

C := 0.2e-1

0.2e-1

 (16)
> 

h := 0.250e-1

0.250e-1

 (17)
> 

nu := .22

.22

 (18)
> 

I1 := (1/3)*w*h^3

0.5207e-5

 (19)
> 

E[0] := A+B

0.569e11

 (20)
> 

nu1 := (1-nu)/((1+nu)*(1-2*nu))

1.142

 (21)
> 

"beta(x,t):=1/(w*h)(W(∑)(-(Pi^(3)*b[n]*(2*n-1)^(3))/(k[n]*8*L^(3))*cos(((2*n-1)*Pi)/(2*L)*x)*(exp(-k[n]*t)))+(R*G*(R*G)^(0.5)*sinh((R*G)^(0.5)*(x-L)))/(cosh((R*G)^(0.5)*L))*t+C*U*(R*G*(R*G)^(0.5)*sinh((R*G)^(0.5)*(x-L)))/(cosh((R*G)^(0.5)*L)))*exp(-W/(C)*t)"

proc (x, t) options operator, arrow; (W*(sum(-(1/8)*Pi^3*b[n]*(2*n-1)^3*cos((1/2)*(2*n-1)*Pi*x/L)*exp(-k[n]*t)/(k[n]*L^3), n = 1 .. 8))+R*G*(R*G)^.5*sinh((R*G)^.5*(x-L))*t/cosh((R*G)^.5*L)+C*U*R*G*(R*G)^.5*sinh((R*G)^.5*(x-L))/cosh((R*G)^.5*L))*exp(-W*t/C)/(w*h) end proc

 (22)
> 

eq := -nu1*I1*a1*((1/2)*E[0]*q(t)+B*lambda*(int(exp(-lambda*(t-s))*q(s), s = 0 .. t)))+2*w*h^2*beta(x, t)

-0.4603e11*q(t)-0.6134e9*(int(exp(-0.170e-1*t+0.170e-1*s)*q(s), s = 0 .. t))+0.5000e-1*(-0.7235e-2*pi*(pi^2+686.)*cos(.4488*x)*exp(-50.*(.3430+pi^2)*t/(pi^2+686.))/(.3430+pi^2)^2-.5860*pi*(9.*pi^2+686.)*cos(1.346*x)*exp(-50.*(.3430+9.*pi^2)*t/(9.*pi^2+686.))/(.3430+9.*pi^2)^2-4.522*pi*(25.*pi^2+686.)*cos(2.244*x)*exp(-50.*(.3430+25.*pi^2)*t/(25.*pi^2+686.))/(.3430+25.*pi^2)^2-17.37*pi*(49.*pi^2+686.)*cos(3.142*x)*exp(-50.*(.3430+49.*pi^2)*t/(49.*pi^2+686.))/(.3430+49.*pi^2)^2-47.47*pi*(81.*pi^2+686.)*cos(4.039*x)*exp(-50.*(.3430+81.*pi^2)*t/(81.*pi^2+686.))/(.3430+81.*pi^2)^2-105.9*pi*(121.*pi^2+686.)*cos(4.937*x)*exp(-50.*(.3430+121.*pi^2)*t/(121.*pi^2+686.))/(.3430+121.*pi^2)^2-206.6*pi*(169.*pi^2+686.)*cos(5.834*x)*exp(-50.*(.3430+169.*pi^2)*t/(169.*pi^2+686.))/(.3430+169.*pi^2)^2-366.3*pi*(225.*pi^2+686.)*cos(6.732*x)*exp(-50.*(.3430+225.*pi^2)*t/(225.*pi^2+686.))/(.3430+225.*pi^2)^2+0.5616e-3*sinh(0.8367e-1*x-.2928)*t+0.1123e-4*Heaviside(t)*sinh(0.8367e-1*x-.2928))*exp(-50.00*t)

 (23)
> 

``


 

Download n-h-ie.mwn-h-ie.mw

How do I calculate inverse laplace of be...

michel_h 15 Maple 2017
May 30 2018
2 1

rho := -2*K*(s+K)^2*k[e]*sinh((s+K)*x/d)/(s*d^2*(4*(s+K)^3*cosh((s+K)*h/d)*h/d^2-4*K*(s+K)*cosh((s+K)*h/d)*h/d+4*sinh((s+K)*h/d)*K))

l.mw

All variables are constant except s and x

Integro-diffrential equation...

michel_h 15 Maple 2017
differential-equation pde pdsolve
January 21 2018
0 0

Hello,

How can i solve this integro-PDE(partial diffrential equation)??

regards...

eq := (1+6*(l/h)^2/(1+nu))*(diff(u(xi, tau), xi, xi, xi, xi)+int(-B*lambda*exp(-lambda(tau-s))*(diff(u(xi, s), xi, xi, xi, xi)), s = 0 .. tau))+diff(u(xi, tau), tau, tau) = alpha*(int((diff(u(xi, tau), xi))^2, xi = 0 .. 1)+int(-B*lambda*exp(-lambda(tau-s))*(int((diff(u(xi, tau), xi))^2, xi = 0 .. 1)), s = 0 .. tau))*(diff(u(xi, tau), xi, xi))+V^2*(sum(j*u(xi, tau)^(j-1), j = 1 .. 8))

jing-Fu.mw

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