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

A. Baddour; Баддур А.; M. M. Gambaryan; Гамбарян М. М.; L. Gonzalez; Гонсалес Л.; M. D. Malykh; Малых М. Д.

doi:10.31857/S013234742302005X

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

Autores: Baddour A.¹, Gambaryan M.¹, Gonzalez L.¹, Malykh M.¹^,2
Afiliações:
1. Peoples’ Friendship University of Russia
2. Joint Institute for Nuclear Research
Edição: Nº 5 (2023)
Páginas: 47-58
Seção: КОМПЬЮТЕРНАЯ АЛГЕБРА
URL: https://journals.rcsi.science/0132-3474/article/view/141782
DOI: https://doi.org/10.31857/S013234742302005X
EDN: https://elibrary.ru/GZBPBR
ID: 141782

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Resumo

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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