Group preserving scheme for the Cauchy problem of the Laplace equation

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 conver...

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Veröffentlicht in:	Engineering analysis with boundary elements 2011-08, Vol.35 (8), p.1003-1009
Hauptverfasser:	Abbasbandy, S., Hashemi, M.S.
Format:	Artikel
Sprache:	eng
Schlagworte:	Cauchy problem Exact sciences and technology Geographic information systems Global Positioning System Group preserving scheme Ill posed problems Ill-posed problem Laplace equation Mathematical analysis Mathematical models Mathematics Method of line Ordinary differential equations Partial differential equations Preserving Satellite navigation systems Sciences and techniques of general use
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Zusammenfassung:	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.
ISSN:	0955-7997 1873-197X
DOI:	10.1016/j.enganabound.2011.03.010