An approach of extrapolation methods for the solution of nonlinear Volterra–Fredholm integral equations of the second kind

Iranian Journal of Numerical Analysis and Optimization

مقاله 3، دوره 15، Issue 1 - شماره پیاپی 32، خرداد 2025، صفحه 54-78   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.85903.1361

نویسندگان

H. Safdari¹؛ M. Moradkhani^{* 1}؛ M.T. Dastjerdi²

¹Faculty of Sciences, Teacher Training Shahid Rajaei University, Lavizan, Tehran, Iran.

²Faculty of Mathematics, Zanjan University, University Boulevard, Zanjan, Iran.

چکیده

This study presents the process of using extrapolation methods to solve the nonlinear Volterra–Fredholm integral equations of the second kind. To do this, by approximating the integral terms contained in equations by a quadrature rule, the nonlinear Volterra–Fredholm integral equations of the second kind are reduced to a set of nonlinear algebraic equations. Then, the solution of the corresponding system of nonlinear equations is approxi-mated by an iterative method, and finally, these iterations are accelerated by an extrapolation method. We demonstrate the effectiveness of the pro-posed approach by solving some numerical examples.

کلیدواژه‌ها

Volterra–Fredholm integral equations؛ Extrapolation methods؛ Iterative methods

مراجع