Analysis of new RET single-step method for solving stiff and singular types of ordinary differential equations

Shaalini, V. J.; Fadugba, S. E.

doi:10.47974/JIM-2336

Open Access Research Article

Analysis of new RET single-step method for solving stiff and singular types of ordinary differential equations

^*V. J. ShaaliniCorresponding authorshaalini.vinci@gmail.comDepartment of MathematicsBishop Heber CollegeTrichy, Tamil Nadu, 620017, India0000-0002-9245-3474View full profile → , S. E. Fadugbasunday.fadugba@eksu.edu.ngDepartment of MathematicsEkiti State UniversityAdo Ekiti, 360001, Nigeria0000-0003-0911-6838View full profile →

* Corresponding author · click or hover a name for details

pp. 169–180Vol. 29Issue 1January 2026DOI: 10.47974/JIM-2336XML

Received:: 05 Mar 2025
Published Online:: 07 Nov 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2336
Pages:: 169–180

Abstract

This study introduces a novel single-step approach that employs an interpolation technique combining a rational function based on a polynomial with a trigonometric interpolation component (RET) for addressing stiff and singular ordinary differential equations (ODEs). The characteristics of the proposed method—such as consistency, convergence, zero stability, and order of accuracy—are thoroughly investigated. To assess its effectiveness, the RET scheme is applied to three distinct numerical problems, and the computed results are evaluated against the corresponding analytical solutions. The findings indicate that RET offers a reliable, precise, and efficient means for numerically solving both stiff and singular ODEs.

Keywords

Analytical solutions Interpolation functions Rational functions combining polynomial and trigonometric polynomials Stiff and singular ordinary differential equations

Subject Classifications

34A1265L0565L2065L70

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