Numerical solution of Gray-Scott system by a low-cost meshless local weak form method

In this paper, the Direct Meshless Local Petrov-Galerkin (DMLPG) procedure is applied for numerical solving of non-linear time-dependent Gray-Scott system. Computational efficiency is the most significant advantage of the DMLPG method in comparison with the classic Meshless Local Petrov-Galerkin (MLPG) method. This is due to the fact that DMLPG shifts the numerical integrations over low-degree polynomials instead of over complicated moving least squares (MLS) shape functions and this reduces the computational costs, significantly. The main aim of this paper is to show that the DMLPG method is also suitable for solving the non-linear time-dependent systems especially Gray-Scott system. It is shown that DMLPG provides considerable savings in computational time in comparison with the classical MLPG method