Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay

被引：5
|
作者：
Zheng, Weishan [1 ]
Chen, Yanping [2 ]
Huang, Yunqing [3 ]
机构：
[1] Hanshan Normal Univ, Coll Math & Stat, Chaozhou 521041, Guangdong, Peoples R China
[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[3] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2019年 / 11卷 / 02期
基金：
美国国家科学基金会;
关键词：
Convergence analysis; Legendre-spectral method; second order Volterra integro-differential equation; delay; error analysis; DIFFERENTIAL EQUATIONS;
D O I：
10.4208/aamm.OA-2018-0121
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both L-2-norm and L-infinity-norm. In the end numerical experiment is illustrated to confirm the theoretical analysis.
引用
收藏
页码：486 / 500
页数：15
相关论文
共 50 条
  • [31] Shifted fractional Legendre spectral collocation technique for solving fractional stochastic Volterra integro-differential equations
    E. H. Doha
    M. A. Abdelkawy
    A. Z. M. Amin
    António M. Lopes
    Engineering with Computers, 2022, 38 : 1363 - 1373
  • [32] A spectral method for a weakly singular Volterra integro-differential equation with pantograph delay
    Weishan Zheng
    Yanping Chen
    Acta Mathematica Scientia, 2022, 42 : 387 - 402
  • [33] A Direct Multi-step Legendre-Gauss Collocation Method for High-order Volterra Integro-differential Equation
    Kajani, M. Tavassoli
    Gholampoor, I.
    APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES (AMITANS'15), 2015, 1684
  • [34] A SPECTRAL METHOD FOR A WEAKLY SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION WITH PANTOGRAPH DELAY
    郑伟珊
    陈艳萍
    Acta Mathematica Scientia, 2022, (01) : 387 - 402
  • [35] A Spectral Method for a Weakly Singular Volterra Integro-Differential Equation with Pantograph Delay
    Zheng, Weishan
    Chen, Yanping
    ACTA MATHEMATICA SCIENTIA, 2022, 42 (01) : 387 - 402
  • [36] Spectral Collocation Methods for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels
    Yin Yang
    Yanping Chen
    Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42 : 297 - 314
  • [37] Numerical solution of Volterra integro-differential equation with delay
    Cimen, Erkan
    Yatar, Sabahattin
    JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2020, 20 (03): : 255 - 263
  • [38] Spectral Collocation Methods for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels
    Yang, Yin
    Chen, Yanping
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (01) : 297 - 314
  • [39] Numerical Approach for Delay Volterra Integro-Differential Equation
    Baharum, Nur Auni
    Majid, Zanariah Abdul
    Senu, Norazak
    Rosali, Haliza
    SAINS MALAYSIANA, 2022, 51 (12): : 4125 - 4144
  • [40] A family of Multistep Collocation Methods for Volterra Integro-Differential Equations
    Cardone, A.
    Conte, D.
    Paternoster, B.
    NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2, 2009, 1168 : 358 - 361
12345