Construction of ‎P‎seudospectral Meshless Radial Point Interpolation for Sobolev Equation with Error Analysis‎

In this study, we develop an approximate formulation for two-dimensional (2D) Sobolev equations based on pseudospectral meshless radial point interpolation (PSMRPI). The Sobolev equations which are arisen in the fluid flow penetrating rocks, soils, or different viscous media do not have an exact solution except in some special cases. The problem can be rigorously solved particularly when the geometry of the domain is more complex. 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. It is proved that the method is convergent and unconditionally stable in some sense with respect to the time. The main results of the Sobolev equation are demonstrated by some examples to show the validity and trustworthiness of the PSMRPI technique.