A new extension of boundary elements method for classical elliptic partial differential equations with constant coefficients |
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| Authors: | H. Hosseinzadeh M. A. Taherkhani |
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| Affiliation: | 1. Department of Mathematics, Persian Gulf University, Bushehr, Iran;2. Department of Mathematics, University of Mazandaran, Babolsar, Iran |
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| Abstract: | This article is devoted to an extension of boundary elements method (BEM) for solving elliptic partial differential equations of general type with constant coefficients. As the fundamental solution of these equations was not available in the literature, BEM was not able to handle them, directly. So the dual reciprocity method (DRM) has been applied to tackle these problems. In this work, a fundamental solution for these equations is obtained and a new formulation is derived to solve them. Besides, we show that the rate of convergence of the new scheme is quadratic when singular (boundary and domain) integrals are calculated, accurately. The new scheme is applicable on complex domains, without needing internal nodes, just same as conventional BEM. So the CPU time of the new scheme is much less than that of the DRM. Numerical examples presented in the article show ability and efficiency of the new scheme in solving two‐dimensional nonhomogenous elliptic boundary value problems, clearly. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2027–2042, 2015 |
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| Keywords: | two‐dimensional elliptic equations boundary elements method fundamental solution singular boundary integrals AMS classification: 65N38 65N06 |
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