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 , J. C., Ogunfiditimi , F., & Sale , I. (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. Retrieved from https://jofresearch.com/index.php/ABAARJ/article/view/140

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