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Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method


Janodi, Mohd Razaie and Abdul Majid, Zanariah and Ismail, Fudziah and Senu, Norazak (2020) Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method. Malaysian Journal of Mathematical Sciences, 14 (2). 191 - 208. ISSN 1823-8343; ESSN: 2289-750X


In this paper, the implementation of one-step hybrid block method with quadrature rules will be proposed for solving linear and non-linear rst order Volterra Integro-Di erential Equations (VIDEs) of the second kind. VIDEs have important applications in many branches of sciences and engineering, such as analysing rhythmic biological data can be conducted by utilizing a curve tting technique based on solutions of the VIDEs. The formulation of the hybrid block method is based on the Lagrange interpolation polynomial. The approximation of the integral part in the VIDEs will be estimated using the quadrature rules. The proposed hybrid block method of order ve will compute the numerical solutions at two points simultaneously at each integration steps. The stability analysis such as order of the method, consistency, zero stable and stability region of the method are deliberated. The xed step size is used to generate the results and the code is written in C language. Numerical simulations are presented to show the e ciency and accuracy of the hybrid method when compared to the Runge-Kutta of order four and ve in terms of accuracy, total steps, and total function calls.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Universiti Putra Malaysia Press
Keywords: Volterra integro-differential equations; Hybrid block method; Quadrature rules; Rhythmic biological data
Depositing User: Mohamad Jefri Mohamed Fauzi
Date Deposited: 07 Jan 2022 08:42
Last Modified: 07 Jan 2022 08:42
URI: http://psasir.upm.edu.my/id/eprint/86934
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