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

Z. Avazzadeh1, Omid Nikan2, J. A. Tenreiro Machado3, Mohammad Navaz Rasoulizadeh4
1Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, 215123, China
2School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
3Institute of Engineering, Polytechnic of Porto, Rua Dr. Antnio B. de Almeida 431, 4249-015, Porto, Portugal
4Department of Mathematics, Velayat University, Iranshahr, Iran

Tóm tắt

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.

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