An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations

Fathalla A. Rihan; Ahmed F. Rihan

doi:10.1155/2022/8961352

An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations

Fathalla A. Rihan
, Ahmed F. Rihan

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ-method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes. The theoretical results are verified by numerical simulations. The theoretical results and numerical simulations show that implicit or partially implicit ϑ-methods, with ϑ>1/2, are effective in resolving stiff pantograph problems.

Original language	English
Article number	8961352
Journal	Complexity
Volume	2022
DOIs	https://doi.org/10.1155/2022/8961352
Publication status	Published - 2022

ASJC Scopus subject areas

General Computer Science
General

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10.1155/2022/8961352

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title = "An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations",

abstract = "The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ-method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes. The theoretical results are verified by numerical simulations. The theoretical results and numerical simulations show that implicit or partially implicit ϑ-methods, with ϑ>1/2, are effective in resolving stiff pantograph problems.",

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AB - The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ-method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes. The theoretical results are verified by numerical simulations. The theoretical results and numerical simulations show that implicit or partially implicit ϑ-methods, with ϑ>1/2, are effective in resolving stiff pantograph problems.

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An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations

Abstract

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