On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation

Abstract

In this study, we develop an approximate formulation for two-dimensional nonlinear Sobolev problems by focusing on pseudospectral meshless radial point interpolation (PSMRPI) which is a kind of locally applied radial basis function interpolation and truthfully a meshless approach. In the PSMRPI method, the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. The convergence and stability of the technique in some sense are studied via some examples to show the validity and trustworthiness of the PSMRPI technique.

A meshless finite point method for the improved Boussinesq equation using stabilized moving least squares approximation and Richardson extrapolation

“…The finite point method (FPM) [32] is a well-known meshless method especially in the field of fluid dynamics. Based on the MLS approximation [23,24,33] and the point collocation technique [34][35][36], the FPM possesses some outstanding merits such as truly meshless, no numerical quadrature, easy to implement, generating sparse and banded discrete systems, and the extensible to high dimensional problems. Theoretical error estimations for the FPM have been established in References [37][38][39].…”