Nystrom-quasilinearization method and smoothing transformation for the numerical solution of nonlinear weakly singular Fredholm integral equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:368

Article

Najafi, Esmaeil¹ 

[1] Urmia Univ, Fac Sci, Dept Math, POB 51818-57561, Orumiyeh, Iran

关键词: Fredholm integral equation;    Nystrom method;    Quasilinearization technique;    Smoothing transformation;   

DOI  :  10.1016/j.cam.2019.112538

来源: Elsevier

【 摘 要 】

In this paper, we introduce and analyse Nystrom-quasilinearization method for the numerical solution of nonlinear weakly singular Fredholm integral equations of the second kind. Under some mild conditions on the equation, applying quasilinearization technique gives a sequence of linear equations with low smooth solutions quadratically convergent to the unique solution of the nonlinear equation. By analysing the behaviour of the solutions near the boundaries and choosing appropriate smoothing transformation, we approximate the solution of the linear equation by Nystrom method. Error analysis of the scheme confirms the improvement of the convergence order in comparison with the case without smoothing transformation. The numerical experiments are in agreement with the theoretical results and show the efficiency of the presented method in comparison with the other methods. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free