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sk04

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PDE Numerical Solution...

sk04 5
November 10 2020
0 0

@tomleslie Thanks for your help.

I'm new to Maple, and I'm sure this next question is trivial, but I would appreciate your help. I'm trying to obtain the numerical solution of the PDE, but I'm getting an error when specifying the initial boundary conditions. I have attached my code.

 

> 

k := 0.1:
sigma := 0.1:
sys:=[diff(y(t), t) = k*y(t), diff(x(r, t), t) = y(t) * exp(r^2/2*sigma^2)];
ibc:={y(0) = 0, x(r, 0) = 0};
pdsymbolic:=pdsolve(sys);
pdnumeric:=pdsolve(sys, ibc, numeric, spacestep = 0.1, time = t, range = 0...5);

[diff(y(t), t) = .1*y(t), diff(x(r, t), t) = y(t)*exp(0.5000000000e-2*r^2)]

  

{x(r, 0) = 0, y(0) = 0}

  

{x(r, t) = 10*_C1*exp((1/10)*t+(1/200)*r^2)+_F1(r), y(t) = _C1*exp(.1*t)}

  

Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector

  
> 

 

Download pdeibc.mw

 

Example...

sk04 5
November 09 2020
0 0

@tomleslie Thanks for your response. This is a basic example of what I’m trying to do:

diff(y(t), t) = k*y(t)

diff(x(r, t), t) = y(t)*exp(r^2/2*sigma^2)

I want to evaluate this first-order ODE as part of the numerical solution for this first-order PDE. The actual equation I'm trying to solve is much more complex than this, so I just tried to give a simple example here.

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