A local reproducing kernel method accompanied by an edge improvement technique for the numerical solution of the 2D Brusselator System

In this paper, the two-dimensional (2D) Brusselator reaction-diffusion system is simulated numerically by a local reproducing kernel method. It is a truly meshless approach which uses the local sub clusters of domain nodes with local basis functions for approximation of fields. It leads to a system of ordinary differential equations (ODEs) for the time-dependent partial differential equations (PDEs). In order to decrease accuracy degradations near boundaries, an edge improvement technique is also used