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Programming and Computer Software

Erschienen in:

01.10.2023

On Implementation of Numerical Methods for Solving Ordinary Differential Equations in Computer Algebra Systems

verfasst von: A. Baddour, M. M. Gambaryan, L. Gonzalez, M. D. Malykh

Erschienen in: Programming and Computer Software | Ausgabe 5/2023

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Abstract

This paper presents an original package for investigating numerical solutions of ordinary differential equations, which is built in the Sage computer algebra system. This project is focused on a closer integration of numerical and symbolic methods while primarily aiming to create a convenient tool for working with numerical solutions in Sage. The package defines two new classes: initial problems and approximate solutions. The first class defines tools for symbolic computations related to initial problems, while the second class defines tools for interpolating values of symbolic expressions on an approximate solution and estimating the error with the use of the Richardson method. An implementation of the Runge–Kutta method is briefly described, with its main feature being the possibility of working with arbitrary Butcher tableaux and arbitrary numeric fields.

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Titel: On Implementation of Numerical Methods for Solving Ordinary Differential Equations in Computer Algebra Systems
verfasst von: A. Baddour
M. M. Gambaryan
L. Gonzalez
M. D. Malykh
Publikationsdatum: 01.10.2023
Verlag: Pleiades Publishing
Erschienen in: Programming and Computer Software / Ausgabe 5/2023
Print ISSN: 0361-7688
Elektronische ISSN: 1608-3261
DOI: https://doi.org/10.1134/S0361768823020044

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