计算数学
       首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  在线办公 | 
计算数学  2017, Vol. 39 Issue (1): 98-114    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |   
一类分数阶多项延迟微分方程的Jacobi谱配置方法
杨水平
惠州学院数学系, 惠州 516007
JACOBI SPECTRAL COLLOCATION METHOD FOR SOLVING A CLASS OF FRACTIONAL MULTI-DELAY DIFFERENTIAL EQUATIONS
Yang Shuiping
Department of mathematics, Huizhou Univerisity, Huizhou 516007, China
 全文: PDF (385 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 本文利用Jacobi谱配置方法数值求解了一类分数阶多项延迟微分方程,并证明了该方法是收敛的,通过若干数值算例验证了相应的理论结果,结果表明Jacobi谱配置方法求解这类方程是非常高效的,同时也为这类分数阶延迟微分方程的数值求解提供了新的选择,对分数阶泛函方程的数值方法的研究有一定的指导意义.
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
关键词分数阶多项延迟微分方程   Jacobi配置方法   误差分析     
Abstract: In this paper,we study Jacobi spectral collocation method for solving the initial value problem (IVP) of a class of fractional multi-delay differential equations.The convergence of the method for this problem is obtained.Some illustrative examples verify our theoretical results successfully.The results of this paper may provide a new good choice for solving fractional delay differential equations.It is believed that these results will be helpful for the further researches on numerical solutions of fractional functional differential equations.
Key wordsfractional multi-delay differential equations   Jacobi spectral collocation method   error analysis   
收稿日期: 2016-07-21;
基金资助:

国家自然科学基金(11501238)、广东省自然科学基金(2016A030313119,2014A030313641)、惠州学院自然科学基金(hzuxl201420)资助项目.

引用本文:   
. 一类分数阶多项延迟微分方程的Jacobi谱配置方法[J]. 计算数学, 2017, 39(1): 98-114.
. JACOBI SPECTRAL COLLOCATION METHOD FOR SOLVING A CLASS OF FRACTIONAL MULTI-DELAY DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2017, 39(1): 98-114.
 
[1] Yu C, Gao G Z. Some results on a class of fractional functional differential equations[J]. Commun. Appl. Nonlinear Anal., 2004, (11)3:67-75.
[2] Zhou Y. Existence and uniqueness of fractional functional differential equations with unbounded delay, International Journal of Dynamical Systems and Differential Equations[J]. 2008, (1)4:239-244.
[3] Zhou Y, Jiao F, Li J. Existence and uniqueness for fractional neutral differential equations with infinite delay[J]. Nonlinear Analysis:Theory, Method and Applications, 2009, (71):3249-3256.
[4] Zhou Y, Jiao F, Li J. Existence and uniqueness for p-type fractional neutral differential equations[J]. Nonlinear Analysis:Theory, Method and Applications, 2009, (71):2724-2733.
[5] Wang J R, Zhou Y. Existence of mild solutions for fractional evolution system[J]. Applied Mathematics and Computation, 2011, (218)2:357-367.
[6] Morgardo M L, Ford N J, Lima P M. Analysis and numerical methods for fractional differential equations with delay[J]. Journal of Computational and Applied Mathematics, 2013, (252):159-168.
[7] Podlubny I. Fractional differential equations[M]. Academic Press, SanDiego, 1999.
[8] Diethelm K and Walz G. Numerical solution of fractional order differential equation by extrapolation[J]. Numer. Algorithms, 1997, (16):231-253.
[9] Diethelm K, Ford N J and Freed Alan D. A predictor-corrector approach for the numerical solution of fractional differential equations[J]. Nonlinear Dynamics, 2002, (29):3-22.
[10] Diethelm K, Ford N J and Reed A D. Detailed error analysis for a fractional Adams method[J]. Numerical Algorithms, Kluwer Academic Publishers, 2004, (36)1:31-52.
[11] El-Mesiry A E M, El-Sayed A M A and El-Saka H A A. Numerical methods for multi-term fractional (arbitrary) orders differential equations[J]. Appl.Math.Comput., 2005, (160)3:683-699.
[12] Arvet Pedas, Enn Tamme. Spline collocation methods for linear multi-term fractional differential equations[J]. Journal of Computational and Applied Mathematics, 2011, (236):167-176.
[13] Pedas A, Tamme E. On the convergence of spline collocation methods for solving fractional differential equations[J]. J. Comput. Appl. Math., 2011, (235):3502-3514.
[14] Li Changpin, Chen An, Ye Junjie, Numerical approaches to fractional calculus and fractional ordinary differential equation[J]. Journal of Computational Physics, 2011, (230):3352-3368.
[15] Li X J, Xu C J. A space-time spectrual method for the time fractional diffusion equation[J]. SIAM Journal of Numerical Analysis, 2009, (47):2018-2131.
[16] Song F Y, Xu C J. Spectral direction splitting methods for two-dimensional space fractional diffusion equations[J]. Journal of Computational Physics, 2015, (299):196-214.
[17] Zhuang P, Liu F. Turner I, et al. Galerkin finite element method and error analysis for the fractional Cable equation[J]. Numeircal Algorithms, 2015, 2016, (72)2:447-466.
[18] Bu W P, Tang Y F, et al. Galerkin finite method for two-dimensional Riesz space fractional diffusion equations[J]. Journal of Computational Physics, 2014, (276):26-38
[19] Chen Y P, Tang T. Spectral methods for weakly singular Volterra integral equations with smooth solutions[J]. Journal of Computational and Applied Mathematics, 2009, (233):938-950.
[20] Chen Y P, Tang T. Convergence analysis of the jacobi spectral-collocation methods for volterra integral equations with a weakly singular kernel[J]. Mathematics of Computation, 201, (79)269:147-167.
[21] Li X J, Tang T, Xu C J. Numerical solutions for weakly singular Volterra integral equations using Chebshev and Legendre Psudo-spectral Galerkin method[J]. Journal of Scientific Computing, 2015, 1-22.
[22] Basim K, Saltani A. Solution of delay fractional differential equations by using linear multistep method[J]. Journal of Kerbala University, 2007, (5)4:217-222.
[23] Sweilam N H, Khader M M, Mahdy A M S. Numerical studies for fractional-order logistic differential equation with deferent delays[J]. J. Appl. Math., 2012(2012), doi:10.1155/2012/764894.
[24] 杨水平. 分数阶比例延迟微分方程的三次样条配置方法[J]. 应用数学, 2014,(27)3:673-678.
[25] 杨水平, 肖爱国. 分数阶延迟微分方程的样条配置方法[J]. 数学的实践与认识,2014, (44)6:247-254.
[26] Zayernouri M, Cao W, Zhang Z, et al. Spectral and Discontinuous Spectral Element Methods for Fractional Delay Equations[J]. Siam Journal on Scientific Computing, 2014, (6)36:B904-B929.
[27] Shen J, Tang T, Wang L L. Spectral methods:Algorithems, Analysis and Applications[M]. Springer-Verlag Berlin Heidelberg, 2011.
[28] Ishtiaq Ali, Hermann Brunner, Tang T. Spectral methods for pantograph-type differential and integral equations with multiple delays[J]. Front. Math. China 2009, (4)1:49-61.
[1] 张根根, 易星, 肖爱国. 求解非线性刚性初值问题的隐显线性多步方法的误差分析[J]. 计算数学, 2015, 37(1): 1-13.
[2] 康彤, 陈涛. 无界区域瞬时涡流问题有限元-边界元耦合的A-φ法的误差分析[J]. 计算数学, 2014, 36(2): 163-178.
[3] 任全伟, 庄清渠. 一类四阶微积分方程的Legendre-Galerkin谱逼近[J]. 计算数学, 2013, 35(2): 125-136.
[4] 李先崇, 孙萍, 安静, 罗振东. 粘弹性方程一种新的分裂正定混合元法[J]. 计算数学, 2013, 35(1): 49-58.
[5] 李宏, 周文文, 方志朝. Sobolev方程的CN全离散化有限元格式[J]. 计算数学, 2013, 35(1): 40-48.
[6] 李宏, 孙萍, 尚月强, 罗振东. 粘弹性方程全离散化有限体积元格式及数值模拟[J]. 计算数学, 2012, 34(4): 413-424.
[7] 张铁, 李铮. 一阶双曲问题间断有限元的后验误差分析[J]. 计算数学, 2012, 34(2): 215-224.
[8] 袁占斌, 聂玉峰, 欧阳洁. 基于泰勒基函数的移动最小二乘法及误差分析[J]. 计算数学, 2012, (1): 25-31.
[9] 腾飞, 孙萍, 罗振东. 抛物型方程基于POD方法的时间二阶中心差的时间二阶精度简化有限元格式[J]. 计算数学, 2011, 33(4): 373-386.
[10] 陈全发, 冯光, 傅尧. 一类分数阶常微分方程初值问题的预校算法[J]. 计算数学, 2009, 31(4): 435-448.
[11] 孙萍, 罗振东, 周艳杰. 热传导对流方程基于POD的差分格式[J]. 计算数学, 2009, 31(3): 323-334.
[12] 刘长河,代西武,汪元伦. 分块三对角方程组的数值解法[J]. 计算数学, 2008, 29(1): 39-48.
[13] 沈智军,袁光伟,沈隆钧. 离散纵标方法诸格式的误差分析[J]. 计算数学, 2002, 24(2): 219-228.

Copyright 2008 计算数学 版权所有
中国科学院数学与系统科学研究院 《计算数学》编辑部
北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发
技术支持: 010-62662699 E-mail:support@magtech.com.cn
京ICP备05002806号-10