Boundary value identification of inverse Cauchy problems in arbitrary plane domain through meshless radial point Hermite interpolation

Abstract

This article presents an efficient method to solve elliptic partial differential equations which are the nucleus of several physical problems, especially in the electromagnetic and mechanics, such as the Poisson and Laplace equations, while the subject is to recover a harmonic data from the knowledge of Cauchy data on some part of the boundary of the arbitrary plane domain. This method is a local nodal meshless Hermite-type collocation technique. In this method, we use the radial-based functions to call out the shape functions that form the local base in the vicinity of the nodal points. We also take into account the Hermit interpolation technique for imposing the derivative conditions directly. The proposed technique called pseudospectral meshless radial point Hermit interpolation is applied on some illustrative examples by adding random noises on source function and reliable results are observed.