Numerical technique for solving generalized integro differential-difference equation with variable coefficient combined ultraspherical-Galerkin method

Adediran D. Adeshola1, Kazeem Issa1, Adam A. Ishaq2, Risikat A. Bello1, Tajudeen O. Aliu1 and Misturah O. Ibrahim2

1Department of Mathematics and Statistics, Kwara State University, Malete, Nigeria.
2Department of Physical Sciences, Al-Hikmah University, Ilorin, Nigeria.

*Corresponding author’s Email: issa.kazeem@kwasu.edu.ng, doi.org/10.55639/607.020100101


ABSTRACT

This study proposes a numerical technique for obtaining approximate solutions to generalized integro-differential-difference equations with variable coefficients using the Ultraspherical–Galerkin method. The method transforms the original equation into a system of algebraic equations. The approximate solution is expressed in terms of shifted ultraspherical polynomials. The stability and convergence of the proposed technique are analyzed. The accuracy and effectiveness of the method are further validated through several benchmark problems selected from the literature.

KEYWORDS

Integro-differential
difference equations,
Ultraspherical-Galerkin
method,
Shifted-ultraspherical
polynomials.

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