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Hi everyone,

I am trying to solve the following dimensionless system of pdes:

u1t=u1x+u2-u1

u2t=3.139uxx-2u2+u3+u1

u3t=-u3x+u2-u3

the boundary conditions are u1(5,t)=0, u2(0,t)=0, u2(5,t)=0, u3=1-heaviside(t-0.1)

initial conditions are u1(x,0)=0, u2(x,0)=0, u3(x,0)=0

pdsolve returns some results but they are not stable. Since I'm fairly new to maple, I don't know if it is possible to discretize...

Calcution-A

with(VectorCalculus):
with(LinearAlgebra):
f := [x3*(1+x2),x1,x2*(1+x1)]:
g := [0,1+x2,-x3]:
fv := <x3*(1+x2),x1,x2*(1+x1)>:
gv := <0,1+x2,-x3>:
ad_f_g :=  MatrixAdd(MatrixVectorMultiply(Jacobian(g,[x1,x2,x3]),fv),-MatrixVectorMultiply(Jacobian(f,[x1,x2,x3]),gv)):
b := <Diff(w(x1,x2,x3),x1),Diff(w(x1,x2,x3),x2),Diff(w(x1,x2,x3),x3)>:
gv := <0,1+x2,-x3>:
c1 := DotProduct(b, gv):
c2 := DotProduct(b, ad_f_g):

Hello,

I am trying to solve the following system of quasilinear PDEs for dependent variables pA(z,t), pB(z,t), pC(z,t) using Maple 14:

> system:= [

.15e-3*diff(pA(z,t),t)+.83e-1*diff(pA(z,t),z)+.47e-3/(1+.11e-6*pA(z,t)+.14e-4*pB(z,t)+.73e-4*pC(z,t))^2*((1+.14e-4*pB(z,t)+.73e-4*pC(z,t))*diff(pA(z,t),t)-.14e-4*pA(z,t)*diff(pB(z,t),t)-.73e-4*pA(z,t)*diff(pC(z,t),t)) = 0,

.15e-3*diff(pB(z,t),t)+.83e-1*diff(pB(z,t),z)+.90e-1/(1+.11e-6*pA(z,t)+.14e-4*pB(z,t...

Hi everyone,

I tried to solve the following system of equations with Maple 15:

You can copy paste the commands below to get the equations

pde1 := [diff(`#msub(mi("n"),mo("&uminus0;"))`(x, t), t) =

diff(`#msub(mi("n"),mo("&uminus0;"))`(x, t), x)+n[o](x, t)-`#msub(mi("n"),mo("&uminus0;"))`(x, t)]

pde2 := [diff(n[o](x, t), t) = 0.3139e-2*(diff(n[o](x, t), x, x))-2*n[o](x, t)+`#msub(mi("n"...

Hi,

I have a PDE system that I keep getting the "pdsolve->Warning: System is inconsistent" message.  Is there a way to see where the contradiction is, i.e. where everything is breaking down.  It is fairly complicated and not easy to eyeball such a thing.

Thanks!

Ryan

Hi,

I have a rather burly system of PDE that I need solved in maple.  It's a little complicated to explain the set-up, but I am solving for some coefficients of a function expansion where each coefficient is solved in terms of some other known functions. 

Basically the problem is the technique and code works perfectly for another application, but it fails me here.  For one, when I try rifsimp(%,[a[0](x,y,t),b[0](x,y,t),c[0](x,y,t)]), it runs for...

I was trying to solve a PDE with boundary conditions and maple 15 didn´t give no answer. 

Is there something wrong? I'm just trying to solve a textbook problem om electrodynamics in maple.

This is the Pde I am trying to solve, with the initial profile function at t=0 called Piinitial, and IC=initialconditions,boundary conditions,

Piinitial := piecewise(r <= 1, (1/9)*r^2+(1/12150)*(31*(8807640902+1170*sqrt(24475122685023))^(2/3)+109499254+22553*(8807640902+1170*sqrt(24475122685023))^(1/3))/(8807640902+1170*sqrt(24475122685023))^(1/3), r <= 2 and 1 < r, (4/405)*(8807640902+1170*sqrt(24475122685023))^(1/3)*r+(14128936/405)*r/(8807640902+1170*sqrt(24475122685023...

I am trying to use Maple to study a 1D wave equation with non-uniform coefficients. In general the problem does not have analytical solutions, hence I am using pdsolve(..., numeric). As the first test I am looking at the development of a Gaussian pulse in a uniform medium, doing:

PDE := diff(u(x, t), t, t) = diff(u(x, t), x, x);

IBC := {u(-10, t) = exp(-(-10)^2), u(10, t) = exp(-10^2), u(x, 0) = exp(-x^2), (D[2](u))(x, 0) = 0};

pds := pdsolve(PDE, IBC,...

I don't know why maple can't solve this PDE

> restart;

> PDE := 4.2000*10^6*(diff(u[1](x, t), t))-.445*(diff(u[1](x, t), x, x))+4200.*u[1](x, t)+464.82-20836.*x-15.832*t+4.0442*10^5*x^2+2953.7*x*t+0.14631e-1*t^2+9.6788*10^6*x^3-2.7139*10^5*x^2*t-.99786*x*t^2+0.15902e-4*t^3-1.0085*10^9*x^4-6.3082*10^6*x^3*t-1069.3*x^2*t^2-0.15006e-1*x*t^3-3.9073*10^(-8)*t^4+2.3478*10^10*x^5+2.5874*10^8*x^4*t+1.2265*10^5*x^3*t^2+2.9028*x^2*t^3+0.17521e-4*x*t^4+1.9407*10^(-11...

I'm trying to solve a PDE using pdsolve() for the Laplace functrion.I can solve the PDE and get a general solution, but when I try to solve the equation with the boundary conditions, Maple indicate that"Error, (in pdsolve/info) wrong extra arguments: {u(0, y) = 0, u(a, y) = 0, u(x, 0) = f(x), u(x, b) = g(x)}"，here is my code:

> restart; with(PDEtools);
> U := diff_table(u(x, y));
> pde[1] := U[`$`(x, 2)]+U[`$`(y, 2)] = 0;
>bc[1] := eval(U[...

I'm using the pdesolve function for a linear pde system of two equations in x and y, with indeterminate functions V(x,y), W(x,y). I'm trying to incorporate Neumann boundary conditions such as:
eval(V[x],x=0) =1;

but when I do so in the pdsolve function I get the error message that the bcs are nonlinear in V and W. Is there a different way that I should be declaring these bcs for use in pdsolve? Or should I in fact be trying to incorporate the bcs some other way?

Hi,

I am trying to solve the following system of ODE's given some initial and final conditions.

Hi,

I am trying to solve a system of PDEs numerically and having following error

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.0):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

Please have a look at attached worksheet and help me out.

Moreover, I want to include boundary conditions are not normal to the boundary. Anyone knows how to do so? Any help would be appreciated.