Application of Newton–Cotes quadrature rule for nonlinear Hammerstein integral equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 8، دوره 11، شماره 2 - شماره پیاپی 20، آذر 2021، صفحه 385-399   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.69824.1024

نویسنده

A. Shahsavaran^*

Department of Mathematics, Borujerd Branch, Islamic Azad University, Borujerd, Iran.

چکیده

A numerical method for solving Fredholm and Volterra integral equations of the second kind is presented. The method is based on the use of  the Newton–Cotes quadrature rule and Lagrange interpolation polynomials. By the proposed method, the main problem is reduced to solve some nonlinear algebraic equations that can be solved by Newton’s method. Also, we prove some statements about the convergence of the method. It is shown that the approximated solution is uniformly convergent to the exact solution. In addition, to demonstrate the efficiency and applicability of the proposed method, several numerical examples are included, which confirms the convergence results.

کلیدواژه‌ها

Fredholm integral equation؛ Volterra integral equation؛ Newton–Cotes quadrature rule؛ Lagrange interpolation؛ Convergence

مراجع