Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation

Abstract

This research work presents a newly truly meshless approach based upon the integrated radial basis functions (IRBFs) technique to study the fractional modified anomalous sub-diffusion equation. First, the temporal direction is discretized by a finite difference method with second-order accuracy. The stability analysis and convergence of the proposed time-discrete formulation are investigated, theoretically. Then, the spatial direction is approximated by the IRBFs methodology. In this approach, the largest-order derivative is approximated by a linear combination of RBFs and then the lower-order derivative and also the unknown function are constructed by repeated integration. According to this procedure, the existing derivatives in the main fractional PDE are approximated smoothly. Furthermore, to show the efficiency of the developed numerical procedure, we employed some non-rectangular computational domains to obtain the numerical results. On the other hand, the mentioned model is solved in one-two-, and three dimensional cases. The numerical results confirm the ability and efficiency of the new numerical method for solving time fractional PDEs on complex computational domains.