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Open Access Research Article

A proposed improved ratio method for the solution of IVPs in delay differential equations of various characteristics

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pp. 1795–1806Vol. 28Issue 5August 2025DOI: 10.47974/JIM-2033XML
Received:
06 Dec 2023
Published Online:
08 Mar 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2033
Pages:
1795–1806

Abstract

This paper proposes an improved Ratio Method (IRM) to tackle Delay Differential Equations (DDEs) by employing a rational-type interpolating function. The Lagrange interpolation was used for approximating the delay argument. The consistency and convergence properties of IRM were analyzed. Moreover, the stability property of IRM using a test problem of DDE was investigated, and the corresponding region of stability was also obtained. The efficiency of IRM was demonstrated through illustrative examples of singularly perturbed and stiff DDEs. A comparative study of the results generated via IRM and that of the theoretical solution was presented. 

Keywords

Subject Classifications

34A1265L0565L2065L70

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