The meshless method for a two-dimensional parabolic problem with a source parameter

In this paper, the reproducing kernel particle method (RKPM) is used for finding the solution of a two-dimensional parabolic inverse problem with a source control parameter, and the corresponding discrete equations are obtained. Comparing with the numerical methods based on mesh, the reproducing kernel particle method only needs the scattered nodes instead of meshing the domain of the problem. The reproducing kernel particle method is an efficient mesh free technique for the numerical solution of partial differential equations. The result of numerical example is presented.

[1]  Mehdi Dehghan,et al.  Finding a control parameter in one-dimensional parabolic equations , 2003, Appl. Math. Comput..

[2]  Afet Golayoglu Fatullayev,et al.  Numerical procedures for determining unknown source parameter in parabolic equations , 2000 .

[3]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[4]  Yanping Lin,et al.  Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations , 1994 .

[5]  Yanping Lin,et al.  An inverse problem of finding a parameter in a semi-linear heat equation , 1990 .

[6]  Weimin Han,et al.  Reproducing kernel element method. Part I: Theoretical formulation , 2004 .

[7]  Afet Golayoglu Fatullayev,et al.  Determination of an unknown source parameter in two-dimensional heat equation , 2004, Appl. Math. Comput..

[8]  Mehdi Dehghan,et al.  Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions , 2006, Math. Comput. Model..

[9]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[10]  Yanping Lin,et al.  Determination of source parameter in parabolic equations , 1992 .

[11]  Mehdi Dehghan,et al.  Parameter determination in a partial differential equation from the overspecified data , 2005, Math. Comput. Model..

[12]  John R. Cannon,et al.  Numerical solutions of some parabolic inverse problems , 1990 .

[13]  Mehdi Dehghan,et al.  Fourth-order techniques for identifying a control parameter in the parabolic equations , 2002 .