Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.

Automated summary

This paper proposes a local meshless radial basis function method to solve the two-dimensional time-fractional Sobolev equation. The method approximates the spatial operator using RBF and uses a finite-difference algorithm for time stepping. The stability of the technique is examined using the matrix method, and numerical examples are provided to verify the method's performance and efficiency.