Some generalized numerical methods for solving higher-order of fractional partial differential equations with application

Mechee, Mohammed Sahib; Aidi, Sameeah H.

doi:10.47974/JIM-1556

Open Access Research Article

Some generalized numerical methods for solving higher-order of fractional partial differential equations with application

^*Mohammed Sahib MecheeCorresponding authormohammeds.abed@uokufa.edu.iqInformation Technology Research and Development Center University of Kufa Information Technology Research and Development Center (ITRDC) University of KufaNajaf, IraqView full profile → , Sameeah H. Aidisameeahaidi9@gmail.comDepartment of Mathematics College of Science University of Baghdad Baghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1391–1400Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1556XML

Published Online:: 28 Oct 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1556
Pages:: 1391–1400

Abstract

This article recommends a computer method for solving some classes of higher-order fractional partial differential equations (FrPDEs). The updated techniques were made by combining the method of lines (MOL) and the numerical RK-type method. For solving certain types of FrPDEs that aren’t in the order, you might expect. Some problems with second-, third-, and fourth-order FrPDEs are solved with the methods made, and the numerical solutions are compared with the analytical answers. Also, a new type of application in classical physics called a wave FrPDE has been made for mechanical waves like water, earthquake, sound, and electromagnetic waves. Many examples are given to show how flexible and useful the method is. The numerical results are seen as the same as the exact solutions of the implementations to show how accurate and useful the suggested methods are. Also, the numerical implementations compare the suggested methods with exact solutions to show that they work and are accurate. The suggested methods used RKM analytical solutions to come up with numerical solutions to the test problems. Some examples are given to show how flexible and useful the method is. Also, the numerical implementations are compared with exact results to show that the proposed methods work and are accurate. R.K. techniques were used to find numerical answers to the suggested test problems.

Keywords

RK RKD Runge-Kutta-Mohammed method (RKM)ODEs Order FrPDEs Finite difference method (FDM)

Subject Classifications

Primary 93A30Secondary 49K15

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