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Research Article Open access CC BY 4.0

Ishikawa-Collocation Method for Nonlinear Fredholm Equations with Non-Separable Kernels

Chinedu Nwaigwe, Azubuike Weli

Journal of Advances in Mathematics and Computer Science · pp. 1–11 · Published 10 Feb 2023

10.9734/jamcs/2023/v38i31747

Abstract

A fixed point method is developed on a mesh for the solution of nonlinear Fredholm equation. First, the problem is collocated at mesh points and a second order quadrature rule is used to approximate the nonlinear integral. Under the assumption of nonexpansivity of self-map, we construct an Ishikawa iteration to linearize the resulting system and approximate the solution at the mesh points. Four numerical examples are given to verify the accuracy and practicability of the method. The results show that indeed the method converges with second order of accuracy. One important lesson from this study is that the results support the claim, in previous studies, that fixed point iterations can provide reliable means of solving several nonlinear problems. It is recommended to extend this work to functional integral equations using higher order quadrature rules.

Integral equations ishikawa iteration discrete xed-point algorithms trapezoidal rule experimental order of convergence

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Cited by 4

Sixth-Order Numerical Solver Based on Truncation Error for Solution of Nonlinear Fredholm Equations

Chinedu Nwaigwe, Azubuike Weli, Dang Ngoc Hoang Thanh · Springer Proceedings in Mathematics & Statistics · 2024

Fourth-Order Trapezoid Algorithm with Four Iterative Schemes for Nonlinear Integral Equations

Chinedu Nwaigwe, Azubuike Weli, Dang Ngoc Hoang Thanh · Lobachevskii Journal of Mathematics · 2023

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