A high-order numerical scheme using orthogonal spline collocation for solving the two-dimensional fractional reaction–subdiffusion equation

Abstract

Abstract In this paper, a high-order numerical scheme is proposed for solving the two-dimensional fractional reaction–subdiffusion equation. The method is based on adopting a third-order weighted and shifted Grünwald difference (WSGD) operator to approximate the time Caputo fractional derivative and applying the orthogonal spline collocation (OSC) method to approximate the spatial derivative. Stability and convergence analysis of the proposed method are rigorously proved. Several numerical examples in one variable and in two space variables are presented to validate our theoretical analysis.

Keywords

• Two-dimensional reaction–subdiffusion equation
• Orthogonal spline collocation
• WSGD operator
• Caputo derivative
• Stability
• Convergence