Paper Info
Title
A high-order numerical method for solving the 2D fourth-order reaction-diffusion equation
Abstract
In the present work, orthogonal spline collocation (OSC) method with convergence order O(τ3−α + hr+ 1) is proposed for the two-dimensional (2D) fourth-order fractional reaction-diffusion equation, where τ, h, r, and α are the time-step size, space size, polynomial degree of space, and the order of the time-fractional derivative (0 < α < 1), respectively. The method is based on applying a high-order finite difference method (FDM) to approximate the time Caputo fractional derivative and employing OSC method to approximate the spatial fourth-order derivative. Using the argument developed recently by Lv and Xu (SIAM J. Sci. Comput. 38, A2699–A2724, 2016) and mathematical induction method, the optimal error estimates of proposed fully discrete OSC method are proved in detail. Then, the theoretical analysis is validated by a number of numerical experiments. To the best of our knowledge, this is the first proof on the error estimates of high-order numerical method with convergence order O(τ3−α + hr+ 1) for the 2D fourth-order fractional equation.
Year
DOI
Venue
2019
10.1007/s11075-018-0509-z
Numerical Algorithms
Keywords
Field
DocType
Fourth-order fractional equation, Orthogonal spline collocation, Finite difference method, Error estimate, 65M12, 65M06, 65M70, 35S10
Convergence (routing),Mathematical analysis,Fourth order,Degree of a polynomial,Mathematical induction,Fractional calculus,Finite difference method,Numerical analysis,Reaction–diffusion system,Mathematics
Journal
Volume
Issue
ISSN
80
3
1572-9265
Citations 
PageRank 
References 
0
0.34
21
Authors
3
Name
Order
Citations
PageRank
Haixiang Zhang16412.19
Xuehua Yang2455.38
Da. Xu37411.27