SOLUTION OF THE TWO-DIMENSIONAL TELEGRAPH EQUATION VIA THE LOCAL RADIAL BASIS FUNCTIONS METHOD

SOLUTION OF THE TWO-DIMENSIONAL TELEGRAPH EQUATION VIA THE LOCAL RADIAL BASIS FUNCTIONS METHOD

S. Niknam, H. Adibi

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Abstract

In the present study, we utilize the local meshless method for solving second order hyperbolic partial di erential equation in two dimensions. First we apply the Crank-Nicolson di erence scheme for the time derivative and the local radial basis functions (LRBFs) collocation method for the spatial derivative. The local approach breaks down the problem domain into subdomains and results small matrix system for each data. Some numerical examples are included to verify the computational e ciency of the proposed method.

Keywords

Radial basis function, Scattered data, Local RBF, Numerical partial di erential equations.