著者

藤原 宏志 今井 仁司 竹内 敏己 磯 祐介

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.15, no.3, pp.419-434, 2005-09-25 (Released:2017-04-08)

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A new method for the direct numerical computation of integral equations of the first kind, of which the integral kernels are analytic, is proposed. The basic idea of the method is based on combination of the spectral collocation method and the multiple precision computation. It gives good numerical results for the equations as far as we don't admit observation errors in the given inhomogeneous terms, and the results implies possibility of numerical analytic continuation on the multiple precision arithmetic. A new accurate rule for numerical integration is also introduced.

著者

竹内 敏己 藤野 清次

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.5, no.1, pp.9-26, 1995

参考文献数

14

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In this paper we study theoretically on some mathematical properties of the matrix of the linear system of equations which stems from discretization of n-dimensional Laplace equation by finite difference approximations. The mathematical properties, i.e., the maximum and minimum absolute eigenvalues, the eigenvectors and the condition numbers of the coefficient matrix A and the Jacobi matrix B of the iterative method are estimated. The discretization by the finite differences in n-dimensions is made using the nearest and skewed neighboring grid points. The effectiveness of the variants of the finite differences is shown throughout this study.