An Effective Dimension-Reducing Technique for Two-Dimensional Nonlinear Space-Fractional Diffusion Equation

Abstract

This work aims to propose an efficient dimension-reducing numerical technique for solving a two-dimensional (2D) nonlinear space-fractional diffusion equation (SFDE). The model problem is initially linearized to enable a more efficient formulation of the numerical scheme. The motive of this work is to establish a splitting technique to reduce the computation cost. This is achieved by partitioning the given 2D model problem into a set of two distinct one-dimensional (1D) problems along both the x and y directions and the error estimate of the proposed scheme is studied. The space-fractional term is approximated utilizing the well-known L1-method over a uniform mesh and thereafter the discrete maximum principle is studied for the discretized scheme. To support the convergence analysis, a suitable discrete barrier function is developed and used. The validity of the theoretical estimations and the proposed numerical technique is demonstrated through numerical experiments.

Keywords

Caputo fractional derivative / Space-fractional diffusion / Dimension-reducing method / L1-method / Discrete maximum principle / Barrier functions / Convergence analysis / 35R11 / 35B51 / 65M06 / 65N12

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