A local meshless collocation method for solving certain inverse problems

In this paper, we propose a meshless scheme based on compactly supported radial basis functions (CS-RBFs) for solving the Cauchy problem of Poisson׳s equation and the inverse heat conduction problems in 2D. By assuming the unknown boundary condition to be a polynomial function, the inverse problems can be solved using a procedure similar to the process for solving forward problems. We employ Tikhonov regularization technique under L-curve regularization parameter to obtain a stable numerical solution. Numerical results verify the effectiveness and stability of this method.