Numerical Verification of Solutions of Periodic Integral Equations with a Singular Kernel |
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| Authors: | Sunao Murashige Shin'ichi Oishi |
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| Affiliation: | 1. Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, 277-8561, Japan
2. Department of Computer and Information Science, School of Science and Engineering, Waseda University, Tokyo, 169-855, Japan
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| Abstract: | This paper proposes the method of numerical verification of solutions of a periodic integral equation with a logarithmic singular kernel, which is typically found in some two-dimensional potential problems. The verification method utilizes a property of the singular integral for trigonometric polynomials, the periodic Sobolev space and Schauder's fixed point theorem. |
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