Piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind in L2
| Autor: | Abdelaziz Mennouni |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Cauchy problem
Cauchy's convergence test Applied Mathematics Mathematical analysis Line integral 010103 numerical & computational mathematics Singular integral 01 natural sciences Computational Mathematics Cauchy principal value 0101 mathematics Cauchy's integral theorem Cauchy matrix Cauchy's integral formula Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 326:268-272 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2017.05.028 |
| Popis: | In this work, we present piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind with constant coefficients in L 2 ( [ 0 , 1 ] , C ) , using a sequence of orthogonal finite rank projections. We prove the existence and uniqueness theorems for the Cauchy integral equation and the approximate equation, respectively. We perform the error analysis for which we give new and improved estimates for the rates of convergence. Numerical example illustrates the theoretical results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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