Automatic Generation of Taylor Series in Pascal-SC: Basic Operations and Applications to Ordinary Differential Equations.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Taylor series have a long history of usefulness in numerical analysis, especially for the numerical solution of the initial value problem for systems of ordinary differential equations. Since recurrence relations for coefficients of Taylor series are well known, it is possible to automate the computation of arithmetic operations and various standard functions with arguments which are themselves series. If the language used for scientific computation supports user defined operators and data types, then the facilities built into the language compiler itself can be used to generate machine code for the evaluation of Taylor coefficients. The Pascal-SC Pascal for Scientific Computation language offers the user highly accurate floating-point and interval arithmetic, the latter being useful for automatic computation of guaranteed error bounds.
- Numerical Mathematics
- Computer Programming and Software