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- Title
Application of Newton-Cotes quadrature rule for nonlinear Hammerstein integral equations.
- Authors
Shahsavaran, A.
- Abstract
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.
- Subjects
NUMERICAL solutions to Fredholm equations; NUMERICAL solutions to Voterra equations; INTEGRAL equations; VOLTERRA equations; NUMERICAL solutions to Lagrange equations
- Publication
Iranian Journal of Numerical Analysis & Optimization, 2021, Vol 11, Issue 2, p385
- ISSN
2423-6977
- Publication type
Article
- DOI
10.22067/ijnao.2021.69824.1024