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

Abstract

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.

A hybrid spectral approach based on 2D cardinal and classical second kind Chebyshev polynomials for time fractional 3D Sobolev equation

“…Moreover, it explains the moisture migration in soil [22] and thermodynamics [23]. In recent years, many numerical methods, such as the local discontinuous Galerkin method [24], local meshless radial basis function method [25], Bernoulli polynomials spectral method [26], and a hybrid technique of the Müntz-Legendre functions and 2D Müntz-Legendre wavelets [27], have been adopted to solve different fractional versions of the Sobolev equation.…”