Abstract
In this article, we deal with non-linear system of higher order Volterra integro-differential equations and their numerical solutions using the Single Term Walsh Series (STWS) method. The connections between STWS coefficients of the unknown functions and its derivatives are derived. The non-linear system of Volterra integro-differential equations are converted into a system of non-linear algebraic equations using the Single Term Walsh Series coefficients. Solving these system of algebraic equations, we obtain the discrete numerical solutions of the non-linear Volterra integro-differential equations. Numerical examples are presented to show the efficiency and applicability of this STWS method for solving the non-linear system of higher order Volterra integro-differential equations.
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One of the authors Mr. R. Chandra Guru Sekar would like to thank National Institute of Technology, Tiruchirappalli, for the financial support through Institute fellowship with Grant Number 1.
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Sekar, R.C.G., Murugesan, K. Numerical Solutions of Non-Linear System of Higher Order Volterra Integro-Differential Equations using Generalized STWS Technique. Differ Equ Dyn Syst 29, 609–621 (2021). https://doi.org/10.1007/s12591-017-0376-4
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DOI: https://doi.org/10.1007/s12591-017-0376-4
Keywords
- Volterra equations
- Integro-differential equations
- Single Term Walsh Series (STWS)
- Numerical methods
- Non-linear systems