Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations

Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations

Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDE...

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Main Authors: Yunfei Li, Shoufu Li
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2021/6633554
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spelling doaj-30176f7eb18f4d9291a83bca12e9c2512021-03-22T00:03:33ZengHindawi LimitedDiscrete Dynamics in Nature and Society1607-887X2021-01-01202110.1155/2021/6633554Classical Theory of Linear Multistep Methods for Volterra Functional Differential EquationsYunfei Li0Shoufu Li1College of Mathematics and PhysicsDepartment of MathematicsBased on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. At last, some numerical experiments verify the correctness of our theories.http://dx.doi.org/10.1155/2021/6633554
collection DOAJ
language English
format Article
sources DOAJ
author Yunfei Li
Shoufu Li
spellingShingle Yunfei Li
Shoufu Li
Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
Discrete Dynamics in Nature and Society
author_facet Yunfei Li
Shoufu Li
author_sort Yunfei Li
title Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
title_short Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
title_full Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
title_fullStr Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
title_full_unstemmed Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
title_sort classical theory of linear multistep methods for volterra functional differential equations
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1607-887X
publishDate 2021-01-01
description Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. At last, some numerical experiments verify the correctness of our theories.
url http://dx.doi.org/10.1155/2021/6633554
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AT shoufuli classicaltheoryoflinearmultistepmethodsforvolterrafunctionaldifferentialequations
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