A Scientific Programming Environment for a Class of Inverse Problems

Bart Childs and Tim McGuire

A prototype scientific programming environment for solving boundary value problems in ordinary differential and integro-differential equations is presented. This environment is designed to assist scientific programmers in overcoming the semantic gap between the formulation of the mathematical model of a physical system and the code for solving that model. The environment includes the following concepts: Knuth’s Literate Programming where the user can document the mathematical model in the TEX or LaTeX system. The use of a Taylor series based integrator which gives efficiency and stability at the cost of higher overhead in code preparation. Symbolic computation to reduce the overhead in the previous item. Most of the environment is based upon the use of a public domain and portable editor (gnu-emacs), [STALLMAN]. This paper specifically addresses the part of conversion of a portion of the TEX code to higher level language (HLL) code such as C FORTRAN. This conversion is tedious and people are not well suited to it. Automating these procedures enables the use of codes that solve these problems with a fraction (3 to 20 percent) of the usual CPU requirements. The higher accuracy requirements gave the best speed improvements. The Taylor series has a characteristic of covering a larger range of the independent variable than the usual Runge-Kutta or multistep methods. This obviously requires a larger fraction of the computation in the generation of the series. This increased computation to communication ratio should be advantageous for parallel computers.

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