Explicit and unconditionally stable algorithms for PDEs

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Posted by Simon on April 15, 1998 at 18:15:30:

Need help/support on further developing "Splitting-up algorithms for PDEs"

Dear Colleagues,

I have developed some new methods for initial/boundary value
problems of PDEs. So far, only tiny part of my research result has
been published due to some reasons (That was the work of couple years
ago). The developed methods have great advantages over those currently
used in solving time-dependent problems. They are:

explicit-no simultaneous equations/no matrices,
computation is node by node stright forward;

second order accurate-reasonably accurate;

unconditionally stable-no restriction on step sizes for the sake of stability.

Besides, they are also naturally parallel algorithms. Obviously,
requirement on memory and CPU time can be significantly reduced because
of the above advantages.Numerical examples are available.

In addition to the above, I am also doing research in other related
areas. In brief, my research consists of several topics:

1) Explicit and unconditionally stable algorithms for solving diffusion
equations in arbitrary regions;

2) Adaptive (explicit, unconditionally stable and second order accurate)
algorithms for hyperbolic equations;

3) Explicit and unconditionally stable algorithms for solving problems
with symmetric coefficient-matrices, such as the Maxwell equations.

4) Study on spectral stability analysis method;

5) ADI methods for solving diffusion equations in arbitrary regions and
stability analysis;

6) Developing a mesh generator and efficient algorithms for solving
elliptic equations;

The importance of this research is obvious. However,I have to say I need to find a university or
institute who may be interested in and willing to support this research.I hope I can have a team or a group to further develop these algorithms and apply them to practical problems.
I have no condition at all (teaching/research, engineering application or
algorithm development) except this research.

I have prepared a report about my research with detailed formulae.
If you can help, please email to


I am also pleased to answer queries about my research.
Thank you very much for your concern and help.



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