Year: 2016
Author: Shuiping Yang, Aiguo Xiao
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 2 : pp. 113–134
Abstract
In this paper, we study the Hermite cubic spline collocation method with two parameters for solving an initial value problem (IVP) of nonlinear fractional differential equations with two Caputo derivatives. The convergence and nonlinear stability of the method are established. Some illustrative examples are provided to verify our theoretical results. The numerical results also indicate that the convergence order is min{4 - α, 4 - β}, where 0 ‹ β ‹ α ‹ 1 are two parameters associated with the fractional differential equations.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1510-m2014-0050
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 2 : pp. 113–134
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Fractional differential equations Caputo derivatives Spline collocation method Convergence Stability.
Author Details
-
Parallel-in-time multigrid for space–time finite element approximations of two-dimensional space-fractional diffusion equations
Yue, Xiaoqiang | Shu, Shi | Xu, Xiaowen | Bu, Weiping | Pan, KejiaComputers & Mathematics with Applications, Vol. 78 (2019), Iss. 11 P.3471
https://doi.org/10.1016/j.camwa.2019.05.017 [Citations: 17] -
Caputo’s Finite Difference Solution of Fractional Two-Point BVPs Using AGE Iteration
Rahman, R. | Ali, N. A. M. | Sulaiman, J. | Muhiddin, F. A.Journal of Physics: Conference Series, Vol. 1123 (2018), Iss. P.012044
https://doi.org/10.1088/1742-6596/1123/1/012044 [Citations: 3] -
Numerical simulation of time fractional Cable equations and convergence analysis
Yang, Yin | Huang, Yunqing | Zhou, YongNumerical Methods for Partial Differential Equations, Vol. 34 (2018), Iss. 5 P.1556
https://doi.org/10.1002/num.22225 [Citations: 15] -
Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem
Okundalaye, Oluwaseun Olumide | Othman, Wan Ainun Mior | Kumaresan, NallasamyAdvances in Mathematical Physics, Vol. 2020 (2020), Iss. P.1
https://doi.org/10.1155/2020/8049397 [Citations: 2] -
Space‐time finite element adaptive AMG for multi‐term time fractional advection diffusion equations
Yue, Xiaoqiang | Liu, Menghuan | Shu, Shi | Bu, Weiping | Xu, YehongMathematical Methods in the Applied Sciences, Vol. 44 (2021), Iss. 4 P.2769
https://doi.org/10.1002/mma.5876 [Citations: 6]