A radial basis meshless method for solving inverse boundary value problems.

In this paper, we develop a new non-iterative numerical method for solving inverse boundary value problems for linear elliptic equations of second order. Here we assume that the Dirichlet and Neumann boundary conditions are given only on part of the domain, we have to reconstruct the solution and its normal derivative on the unaccessible part of the domain, which is the well-known ill-posed Cauchy problem. We propose to solve such inverse problems directly by using the recently developed radial basis meshless method. Several numerical experiments are given to demonstrate the effectiveness and efficiency of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]