Intelligent Techniques in the Solution of Nonlinear Differential Equations

Richard L. Peskin

The integration of symbolic computation with numeric computation is a software direction that offers considerable potential, not only in terms of improved performance, but also for effecting solution verification and completeness. This note discusses issues associated with the incorporation of mathematical knowledge into the symbolicnumeric computation process. The problem considered is the stiff nonlinear boundary value differential equation problem. Methods to employ symbolic computing, together with use of a specialized mathematical knowledge base allow this type of problem to be solved with much greater efficiency than with typical "brute force" numerical methods. In addition, the methodology assures identification of all stable solutions, and problem based parallelism is identified. Challenges associated with extending these concepts to other classes of problems are discussed.

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