An improved localized radial basis-pseudospectral method for solving fractional reaction–subdiffusion problem

The fractional reaction–subdiffusion problem is one of the most well-known subdiffusion models extensively used for simulating numerous physical processes in recent years. This paper introduces an efficient local hybrid kernel meshless procedure to approximate the time fractional reaction–subdiffusion problem involving a Riemann–Liouville fractional derivative. This technique is based on a central difference approach in the temporal direction and the hybridization of the cubic and Gaussian kernels in the spatial direction. The main idea of this hybridization is to develop a kernel that benefits from the advantages of two different kernels and avoids their limitations, while maintaining the global collocation method. This local approach considers only neighboring collocation nodes and it does not produces ill-conditioning that occurs in other methods with large dense matrix systems. The time discrete scheme in terms of the unconditional stability and convergence is analyzed. Numerical examples are presented to show the validity, effectiveness and accuracy of the method.