DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Mohammad ZAREBNIA; Reza PARVAZ; Amir SABOOR BAGHERZADEH

doi:10.1016/S0252-9602(18)30817-8

Acta mathematica scientia, Series B >

2018 , Vol. 38 >Issue 4: 1322 - 1344

DOI: https://doi.org/10.1016/S0252-9602(18)30817-8

Articles

DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Mohammad ZAREBNIA ,
Reza PARVAZ ,
Amir SABOOR BAGHERZADEH

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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 date: 2016-05-12

Revised date: 2017-09-16

Online published: 2018-08-25

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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(h^m+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

Cite this article

Mohammad ZAREBNIA , Reza PARVAZ , Amir SABOOR BAGHERZADEH . DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia, Series B, 2018 , 38(4) : 1322 -1344 . DOI: 10.1016/S0252-9602(18)30817-8

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