期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 436, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.cam.2023.115365
关键词
Chebyshev polynomial; Numerical method; Error bound; Order of convergence; Cauchy system of integral equation
In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
In this paper, we develop Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations of index minus N using Chebyshev polynomials of the first and second kind, where N is the total number of Cauchytype singular integral equations in the system. Without theoretical analysis, a numerical scheme is not justified. Therefore, first, we prove the well-posedness of the system of Cauchy-type singular integral equations with the help of the compactness of an operator. Further, we derive a theoretical error bound and the order of convergence. Also, we show that the resulting system of equations obtained by applying the algorithm is well-posed together with an explicit representation of the solution in matrix form. Finally, we give some illustrative examples to validate the theoretical error bounds numerically. (c) 2023 Elsevier B.V. All rights reserved.
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