Derivation of Continuous Linear Multistep Hybrid Block Method for the Solution of Volterra Integral Equation of Second Kind

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Published: 2024-06-18

Page: 59-69


John Chuseh Ahmadu

Department of Mathematics, University of Abuja, Nigeria.

F.O. Ogunfiditimi *

Department of Mathematics, University of Abuja, Nigeria.

I. Sale

Department of Mathematics, University of Abuja, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

In this paper, we proposed a continuous linear multistep hybrid block method for the solution of Volterra integral equation of second kind of the form y(x) = f (x) +  \(f^{xn}_{xo}\) \(\varphi\)(x, s)y(s))ds, using power series and trigonometrically fitted function as the trial solution for the approximation via collocation techniques. The proposed hybrid block scheme is found to be consistent, zero-stable and convergent. The implementation of the scheme on numerical problems and comparisons of results obtained with existing numerical method will be included.

Keywords: Multistep hybrid block method, power series, collocation and interpolation method, second kind of Volterra integral equations


How to Cite

Ahmadu , John Chuseh, F.O. Ogunfiditimi, and I. Sale. 2024. “Derivation of Continuous Linear Multistep Hybrid Block Method for the Solution of Volterra Integral Equation of Second Kind”. Asian Basic and Applied Research Journal 6 (1):59-69. https://jofresearch.com/index.php/ABAARJ/article/view/140.

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