jam_27
04-24-2006, 12:49 PM
I need the possible & stable numerical methods for solving the following PDE: Its a nonlinear parabolic boundary value problem.I don’t want accumulated numerical errors as I am investigating an instability in the bigger code involving a lot of iterations.This PDE is a part of the bigger code
The PDE is :
d(N(x,t))/dt=D*d2(N(x,t))/dx2-A*N(x,t)-B*N2(x,t)-C*N3(x,t)-S(x,t)+ R(x)
N(x=a,t)=N(x=b,t)=0 for all t. N(x,t=0)=f(x) . (f(x) is a Gaussian function)
where N2 is N-squared, N3 is N-cube and so on. S(x,t) can be a rapidly oscillating function in x and t. C is very small as compared to the other constants A, B and D (all positive).
Is it possible to use a relaxation method for solving the above PDE? I ask this because the corresponding steady state problem can be solved very effectively using a Relaxation method and I have a efficient code for that already.
Please also give me a reference with your suggestions so that I can refer it. Please ask me if you need any more information about the PDE.
Thanks for the help in advance and for having such a great forum.
Jam
The PDE is :
d(N(x,t))/dt=D*d2(N(x,t))/dx2-A*N(x,t)-B*N2(x,t)-C*N3(x,t)-S(x,t)+ R(x)
N(x=a,t)=N(x=b,t)=0 for all t. N(x,t=0)=f(x) . (f(x) is a Gaussian function)
where N2 is N-squared, N3 is N-cube and so on. S(x,t) can be a rapidly oscillating function in x and t. C is very small as compared to the other constants A, B and D (all positive).
Is it possible to use a relaxation method for solving the above PDE? I ask this because the corresponding steady state problem can be solved very effectively using a Relaxation method and I have a efficient code for that already.
Please also give me a reference with your suggestions so that I can refer it. Please ask me if you need any more information about the PDE.
Thanks for the help in advance and for having such a great forum.
Jam