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

Hi all,

Please help me out with this.

Please see the attached PDF document (if I uploaded it properly) or download the thesis form the link below.

http://www.iis.ee.ethz.ch/~laser/pdf-downloads/dip_lutz.pdf

The author uses a 'Thomas' algorithm to solve his PDE. I could not find it in NR in FOTRAN, which he refers to.

Also can someone please tell me, where can I find the central difference scheme used by the author of this thesis? Its really interesting for me (I am new to Numerical Analysis) . I am especially interested in the book this author referred with the specific notation. Can anyone identify it. The author again refers to the same book: NR in FORTRAN, The art of scientific Computing (2nd edition), CUP, 1992. Please tell me.

Thanks,

Jam