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Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Convergent piecewise series solutions of ordinary differential equations

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pp. 1599–1614Vol. 27Issue 7November 2024DOI: 10.47974/JIM-2001XML
Received:
07 Nov 2023
Published Online:
30 Nov 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-2001
Pages:
1599–1614

Abstract

The series approximations of ordinary differential equations usually possess a limited validity range. Outside the convergence interval, the solution does not comply with the real solution. A technique is proposed in this work to expand the validity interval of the series approximations. Solutions are constructed in the vicinity of several points and are joined to each other with satisfaction of the continuity conditions. By employing the piecewise series solutions, the validity range of the approximations can be made to cover the whole domain of interest. In constructing a single analytical expression from the piecewise series, the Gamma Interval function is used. Sample problems of first, second and third order are attacked with the proposed method and comparisons with the numerical and exact solutions are given. It is shown that the method can be effectively used in constructing approximate solutions of ordinary differential equations.

Keywords

Subject Classifications

34A1234A2534A3434A45

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