WSEAS Transactions on Mathematics

Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018

A Way for Finding the Relation Between of the Degree and Order for Multistep Method Used to Applied to Solving of the Volterra Integro-Differential Equation

AUTHORS: Mehdiyeva Galina, Ibrahimov Vagif, Imanova Mehriban

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ABSTRACT: As is known there are some classes of numerical methods have constructed to solving initial value problem of the ODE, which fundamentally investigated by the many known scientist. Therefore the specialists tried to study many scientific and applied problems by using these methods. Here we have defined the direct way between the initial value problem for the Volterra integro-differential and Ordinary Differential Equations. By using this way have constructed the multistep methods with constant coefficients, which are applied to solving initial value problem for the Volterra integro-differential equations and have determined the necessary and sufficient conditions for its convergence. And also have proven that the constructed here methods are more accurately than the known, which is illustrated by the application of concrete method to solving of the model problem.

KEYWORDS: Volterra Integro-Differential Equations, initial value problem of the ODE, multistep methods (MM), stability and degree for MM


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WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #20, pp. 155-161

Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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