Solving Volterra Integro-Differential Equations involving Delay: A New\n Higher Order Numerical Method

2020/09/24 by Aman Jhinga, Jhinga, Aman, Jayvant Patade +3
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2009.11571

openalex publication_date 2020/09/24 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28

Abstract

The aim of the present paper is to introduce a new numerical method for\nsolving nonlinear Volterra integro-differential equations involving delay. We\napply trapezium rule to the integral involved in the equation. Further,\nDaftardar-Gejji and Jafari method (DGJ) is employed to solve the implicit\nequation. Existence-uniqueness theorem is derived for solutions of such\nequations and the error and convergence analysis of the proposed method is\npresented. We illustrate efficacy of the newly proposed method by constructing\nexamples.\n

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