On the numerical solution of second order delay differential equations via a novel approach

Volume 36, Issue 1, pp 1--16 https://dx.doi.org/10.22436/jmcs.036.01.01

Publication Date: June 14, 2024 Submission Date: April 14, 2024 Revision Date: April 20, 2024 Accteptance Date: May 19, 2024

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Authors

S. Aljawi - Department of Mathematical Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, P.O. Box 84428, Saudi Arabia. Kamran - Department of Mathematics, Islamia College Peshawar, Peshawar 25120, Khyber Pakhtoonkhwa, Pakistan. S. Hussain - Department of Mathematics, Islamia College Peshawar, Peshawar 25120, Khyber Pakhtoonkhwa, Pakistan. K. Shah - Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia. Th. Abdeljawad - Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.

Abstract

Delay differential equations belong to an important class of differential equations in which the evolution of the state depends on the previous time. This work proposes a novel approach for the numerical solution of delay differential equations of second order. The suggested numerical scheme is based on Laplace transform (LT) technique. In the suggested technique, first, the given equation is transformed using the LT method to an algebraic expression. The expression is then solved for the unknown transformed function and finally the well-known Weeks method is utilized to convert the solution back to time domain. Functional analysis was used to examine the existence and uniqueness of the considered equations and to generate sufficient requirements for Ulam-Hyers (UH) type stability. Furthermore, we consider different numerical example from literature to validate our method.

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Keywords

• Delay differential equation
• Laplace transform
• uniqueness and existence
• Ulam-Hyers stability
• Weeks method

MSC

•  44A10
•  34A12
•  65Lxx

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