An effective collocation technique to solve the singular Fredholm integral equations with Cauchy kernel

Advances in Difference Equations

Ali Seifi¹  Tofigh Allahviranloo¹  Taher Lotfi¹  Mahmoud Paripour¹ 

[1] Department of Mathematics, Islamic Azad University, Hamedan Branch, Iran

关键词: collocation method;    singular integral equation;    Cauchy kernel;    Bernstein polynomial;   

DOI  :  10.1186/s13662-017-1339-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, an effective numerical method to solve the Cauchy type singular Fredholm integral equations (CSFIEs) of the first kind is proposed. The collocation technique based on Bernstein polynomials is used for approximation the solution of various cases of CSFIEs. By transforming the problem into systems of linear algebraic equations, we see that this approach is computationally simple and attractive. Then the approximate solution of the problem in truncated series form is obtained by using the matrix form of this method. Convergence and error analyses of the presented method are mentioned. Finally, numerical experiments show the validity, accuracy, and efficiency of the proposed method.

【 授权许可】

CC BY