A Unified Meshfree Pseudospectral Method for Solving Both Classical and Fractional PDEs

In this paper, we propose a meshfree method based on the Gaussian radial basis function (RBF) to solve both classical and fractional PDEs. The proposed takes advantage of analytical Laplacian functions so as accommodate discretization in single framework avoid large computational cost for numerical evaluation derivatives. These important merits distinguish it from other methods Moreover, our is simple easy handle complex geometry local refinement, its computer program implementation remains same any dimension $d \ge 1$. Extensive experiments are provided study performance approximating Dirichlet Laplace operators solving PDE problems. Compared recently Wendland RBF method, exactly incorporates boundary conditions into scheme free Gibbs phenomenon observed literature. Our studies suggest that obtain good accuracy shape parameter cannot be too small or big, optimal might depend center points solution properties.