Numerical solution of Fredholm and Volterra integral equations using the normalized Müntz−Legendre polynomials

Iranian Journal of Optimization

دوره 14، شماره 1، خرداد 2022، صفحه 1-13   

نوع مقاله: Research Paper

نویسندگان

Fereshteh Saemi؛ Hamideh Ebrahimi^* ؛ Mahmoud Shafiee

Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

چکیده

The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operational matrices, a system of algebraic equations is derived that can be readily handled through the use of the Newton scheme. The stability, error bound, and convergence analysis of the method are discussed in detail by preparing some theorems. Several illustrative examples are provided formally to show the efficiency of the proposed method.

کلیدواژه‌ها

Nonlinear Fredholm and Volterra integral equations؛ Müntz-Legendre polynomials؛ Spectral method؛ Operational matrix؛ Stability, error bound, and convergence analysis

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