A robust numerical method for a fractional differential equation

作者：Cen, Zhongdi; Le, Anbo^*; Xu, Aimin

来源：Applied Mathematics and Computation, 2017, 315: 445-452.

DOI：10.1016/j.amc.2017.08.011

• Fractional differential equation
• Caputo fractional derivative
• Volterra integral equation
• Adapted mesh
• Convergence analysis

This paper is devoted to giving a rigorous numerical analysis for a fractional differential equation with order alpha is an element of (0, 1). First the fractional differential equation is transformed into an equivalent Volterra integral equation of the second kind with a weakly singular kernel. Based on the a priori information about the exact solution, an integral discretization scheme on an a priori chosen adapted mesh is proposed. By applying the truncation error estimate techniques and a discrete analogue of Gronwall's inequality, it is proved that the numerical method is first-order convergent in the discrete maximum norm. Numerical results indicate that this method is more accurate and robust than finite difference methods when alpha is close to 0.

• 出版日期2017-12-15
• 单位浙江万里学院; 宁波大红鹰学院