Numerical method for the solution of high order Fredholm integro-differential difference equations using Legendre polynomials

Document Type : Research Article

Authors

• P.T. Pantuvo ¹
• G. Ajileye ¹
• R. Taparki ²
• O.O. Aduroja ³

¹ Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

² Department of Mathematical Sciences, Taraba State University, Jalingo, Taraba State, Nigeria.

³ Department of Mathematics, University of Ilesa, Ilesa, Osun State, Nigeria.

10.22067/ijnao.2024.87599.1425

Abstract

This research paper deals with the numerical method for the solution of high-order Fredholm integro-differential difference equations using Legen-dre polynomials. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the collocation method. We then solve the algebraic equation using Newton’s method. We establish the uniqueness and convergence of the solution. Numerical problems are considered to test the efficiency of the method, which shows that the method competes favorably with the existing methods and, in some cases, approximates the exact solution.

Keywords

• Collocation
• Fredholm
• Integro-differential
• Linear and nonlin-ear
• Approximate solution

Main Subjects

• Numerical Analysis

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