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I have the following PDE

PDE: u

BC: u

u

u

u(x,0,t)=0

IC: u(x,y,0)=0

I've set up my ODEs using seperation of variables to get

X''/X=k

where k

How do I account for my source term (f(x,y,t))? I'm reading up on eigenfunction expansion but so far it's only for the dimensional case.

PDE: u

_{t}=A^{2}(u_{xx}+u_{yy})+f(x,y,t) such that A is a constantBC: u

_{x}(1,y,t)=0u

_{x}(0,y,t)=0u

_{y}(x,1,t)=0u(x,0,t)=0

IC: u(x,y,0)=0

I've set up my ODEs using seperation of variables to get

X''/X=k

_{1}Y''/Y=k_{2}T'/(A^{2})T=k_{1}+k_{2}where k

_{1}and k_{2}are constants.How do I account for my source term (f(x,y,t))? I'm reading up on eigenfunction expansion but so far it's only for the dimensional case.

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