DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

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

Acta mathematica scientia,Series B ›› 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. 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

Abstract

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

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.

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References 11

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DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

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