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

Iranian Journal of Numerical Analysis and Optimization

مقاله 8، دوره 14، Issue 3 - شماره پیاپی 30، آذر 2024، صفحه 833-874   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.87599.1425

نویسندگان

P.T. Pantuvo¹؛ G. Ajileye^{* 1}؛ R. Taparki²؛ O.O. Aduroja³

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

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

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

چکیده

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.

کلیدواژه‌ها

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

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