## Application of Collocation Methods for a Hybrid Block Scheme for the Solution of Volterra Intregral Equation of the Second Kind

Published: 2024-03-11

Page: 118-131

J. A. Chuseh *

Department of Mathematics, University of Abuja, Nigeria.

B. B. Rakiatou

Baze University Abuja, Nigeria.

Department of Mathematics, Federal University Wukari, Nigeria.

A. Ibrahim

Department of Mathematics, University of Abuja, Nigeria.

S. A. Kambai

Department of Mathematics, University of Abuja, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

In this paper, a class of three-step implicit second order hybrid block methods for the solutions of Volterra integral equation of the second kind has been developed, using the interpolation and collocation approach. The discrete block methods were recovered when the continuous block methods were evaluated at all step points. The block methods used to implement the main method guaranteed that each discrete scheme obtained from the simultaneous solution of the block has the same order of accuracy as the main continuous method. Hence, the new class of k-step methods gives high order of accuracy with very low error. The basic properties of the methods were investigated and the methods were found to be consistent, zero-stable and convergent.

Keywords: Collocation method, power series, hybrid block, discrete scheme, Volterra integral equation of second kind (VIE)

#### How to Cite

Chuseh , J. A., Rakiatou , B. B., Adu , A., Ibrahim , A., & Kambai , S. A. (2024). Application of Collocation Methods for a Hybrid Block Scheme for the Solution of Volterra Intregral Equation of the Second Kind. Asian Journal of Pure and Applied Mathematics, 6(1), 118–131. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1964

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