Method of lines and Runge-Kutta method for solving delayed one dimensional transport equation

Volume 28, Issue 3, pp 270--280 http://dx.doi.org/10.22436/jmcs.028.03.05

Publication Date: June 26, 2022 Submission Date: March 28, 2022 Revision Date: May 08, 2022 Accteptance Date: May 20, 2022

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Authors

S. Karthick - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603 203, Tamilnadu, India. R. Mahendran - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603 203, Tamilnadu, India. V. Subburayan - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603 203, Tamilnadu, India.

Abstract

In this article we consider a delayed one dimensional transport equation. The method of lines with Runge-Kutta method is applied to solve the problem. It is proved that the present method is stable and convergence of order \(O(\Delta t+\bar{h}^{4})\). Numerical examples are presented to illustrate the method presented in this article.

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Keywords

• Stable method
• Runge-Kutta method
• transport equation
• method of lines

MSC

•  34K10
•  35B50
•  35F10
•  65M06
•  65M12
•  65M15

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