Abstract
A local meshless method is applied to find the numerical solutions of two classes of inverse problems in parabolic equations. The problem is reconstructing the source term using a solution specified at some internal points; one class is that the source term is time dependent, and the other class is that the source term is time and space dependent. Some numerical experiments are presented and discussed.
Highlights
The inverse problem of parabolic equations appears naturally in a wide variety of physical and engineering settings; many researchers solved this problem using different methods [1]-[10]
An important class of inverse problem is reconstructing the source term in parabolic equation, and it has been discussed in many papers [11]-[19]
To overcome the problems of ill-conditioned and the shape parameter sensitivity in radial basis functions method, the local radial basis function was introduced by Lee et al [22]; in contrast to radial basis functions method, only scattered data in the neighboring points are used in local radial basis functions, instead of using all the points, the order of the matrix which is obtained from discretization being reduced, so the matrix of shape function is sparse
Summary
College of Computer Engineering and Applied Mathematics, Changsha University, Changsha, China.
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