This paper examines the numerical solution of the nonlinear coupled Burger’s equations with various values of viscosity by local meshless methods. The local radial basis functions collocation method (LRBFCM) belongs to the class of truly meshless methods which do not need any underlying mesh but work on a set of uniform or random nodes only, without any a priori node to node connectivity. The n...

In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis ...

The paper provides a computational technique that allows to compare all linear methods for PDE solving that use the same input data. This is done by writing them as linear recovery formulas for solution values as linear combinations of the input data, and these formulas are continuous linear functionals on Sobolev spaces. Calculating the norm of these functionals on a fixed Sobolev space will t...

The Moving Least Squares method (MLS) provides an approximation û of a function u based solely on values u(xj) of u on scattered ”meshless” nodes xj . Derivatives of u are usually approximated by derivatives of û. In contrast to this, we directly estimate derivatives of u from the data, without any detour via derivatives of û. This is a generalized Moving Least Squares technique, and we prove t...