Numerical solution of nonlinear sine-Gordon equation with local RBF-based finite difference collocation method

This paper presents the local radial basis function based on finite difference (LRBF-FD) for the sine-Gordon equation. Advantages of the proposed method are that this method is mesh free unlike finite difference (FD) and finite element (FE) methods, and its coefficient matrix is sparse and well-conditioned as compared with the global RBF collocation method (GRBF). Numerical results show that the LRBF-FD method has good accuracy as compared with GRBF