Inverse Cauchy problem of annulus domains in the framework of spectral meshless radial point interpolation

Abstract

In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the Cauchy problems of two-dimensional elliptic PDEs in annulus domains. Unknown data on the inner boundary are obtained while overspecified boundary data are imposed on the outer boundary using the SMRPI. The SMRPI employs monomials and radial basis functions (RBFs) through interpolation and applies them locally with the help of spectral collocation ideas. In this way, localization in SMRPI can reduce the ill-conditioning for Cauchy problem. Furthermore, we improve previous results and overcome the ill-conditioning of Cauchy problem. It is revealed the SMRPI is more accurate and stable by adding strong perturbations.