Title

Stability and Accuracy Analysis of θ Scheme for a Convolutional Integro-Differential Equation

Document Type

Article

Publication Date

7-1-2020

Subject Area

ARRAY(0x55c826f12348)

Abstract

Spatially long-range interactions for linearly elastic media resulting in dispersion relations are modelled by an integro-differential equation of convolution type (IDE) that incorporate non-local effects. This type of IDE is nonstandard (hence, it is almost impossible to obtain exact solutions) and plays an important role in modeling various applied science and engineering problems. In this article, such an IDE describing a linear elastic wave phenomenon has been studied. First, a discrete equivalent of the model IDE in space is proposed and then a class of forward backward average one step θ scheme for the semi-discrete time dependent numerical method has been developed. Further, stability and accuracy of the developed method has been analyzed rigorously.

Publication Title

Differential Equations and Dynamical Systems

Volume

28

Issue

3

First Page

633

Last Page

646

Digital Object Identifier (DOI)

10.1007/s12591-019-00476-w

ISSN

09713514

E-ISSN

09746870

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