A Meshfree Computational Approach Based on Multiple-Scale Pascal Polynomials for Numerical Solution of a 2D Elliptic Problem with Nonlocal Boundary Conditions

Abstract

A two-dimensional (2D) elliptic problem with nonlocal boundary conditions on both regular and irregular domains is solved numerically by Pascal polynomial basis unified with multiple-scale technique. Very accurate numerical solutions and quite reasonable condition numbers are obtained with the proposed method which is also a truly meshfree method since difficult meshing processes or numerical integrations over domains are not needed for considered problems. Four test problems are solved to show the accuracy and efficiency of the proposed method. Also stability of the method is studied against large noise effect.