数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1322-1344.doi: 10.1016/S0252-9602(18)30817-8

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DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Mohammad ZAREBNIA1, Reza PARVAZ1, Amir SABOOR BAGHERZADEH2   

  1. 1. Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran;
    2. Department of Applied Mathematics, Faculty of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
  • 收稿日期:2016-05-12 修回日期:2017-09-16 出版日期:2018-08-25 发布日期:2018-08-25
  • 通讯作者: Mohammad ZAREBNIA,E-mail:zarebnia@uma.ac.ir E-mail:zarebnia@uma.ac.ir
  • 作者简介:Reza PARVAZ,E-mail:rparvaz@uma.ac.ir;Amir SABOOR BAGHERZADEH,E-mail:saboorbagherzadeh.a@gmail.com

DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Mohammad ZAREBNIA1, Reza PARVAZ1, Amir SABOOR BAGHERZADEH2   

  1. 1. Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran;
    2. Department of Applied Mathematics, Faculty of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
  • Received:2016-05-12 Revised:2017-09-16 Online:2018-08-25 Published:2018-08-25
  • Contact: Mohammad ZAREBNIA,E-mail:zarebnia@uma.ac.ir E-mail:zarebnia@uma.ac.ir

摘要:

In this paper, we study an efficient asymptotically correction of a-posteriori error estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integrodifferential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O(hm+1) as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.

关键词: Volterra integro-differential, defect correction principle, piecewise polynomial, collocation, finite difference, error analysis

Abstract:

In this paper, we study an efficient asymptotically correction of a-posteriori error estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integrodifferential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O(hm+1) as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.

Key words: Volterra integro-differential, defect correction principle, piecewise polynomial, collocation, finite difference, error analysis