RBF-Based Local Meshless Method for Fractional Diffusion Equations

The fractional diffusion equation is one of the important recent models that can efficiently characterize various complex processes, such as in inhomogeneous or heterogeneous media porous media. This article provides a method for numerical simulation time-fractional equations. proposed scheme combines local meshless based on radial basis function (RBF) with Laplace transform. first implements transform to reduce given problem time-independent domain, and then RBF-based utilized obtain solution reduced domain. Finally, Stehfest’s convert from domain into real uses handle order derivative, which avoids computation convolution integral derivative overcomes effect time-stepping stability accuracy. tested using four examples. All results demonstrate easy implement, accurate, efficient has low computational costs.