Group preserving scheme for the Cauchy problem of the Laplace equation |
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Authors: | S. Abbasbandy M.S. Hashemi |
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Affiliation: | 1. Department of Mathematics, Imam Khomeini International University, Ghazvin 34149, Iran;2. Bonab University, Bonab 55517, Iran |
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Abstract: | In this paper, we consider the Cauchy problem for the Laplace equation by group preserving scheme (GPS) which is an ill-posed problem, because the solution does not depend continuously on the data. For this, the Laplace equation, by using a semi-discretization method namely method of line, is converted to an ODEs system and then obtained ODEs system is considered by GPS. Stability of GPS for ill-posed Laplace equation is shown. The problem numerical results show the efficiency and power of this method. |
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