Application of compact local integrated RBFs technique to solve fourth-order time-fractional diffusion-wave system

Abbaszadeh, Mostafa; Bagheri Salec, AliReza; Jebur, Alaa Salim

doi:10.22124/jmm.2024.25417.2260

Application of compact local integrated RBFs technique to solve fourth-order time-fractional diffusion-wave system

Document Type : Research Article

Authors

¹ Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran

² Department of Mathematics, Faculty of Basic Scince, University of Qom, Alghadir Blvd., Qom, Iran

10.22124/jmm.2024.25417.2260

Abstract

The main aim of the current paper is to apply the compact local integrated RBFs technique to the numerical solution of the fourth-order time-fractional diffusion-wave system. A finite difference formula is employed to obtain a time-discrete scheme. The stability and convergence rate of the semi-discrete plan are proved by the energy method. A new unknown variable is defined to obtain a second-order system of PDEs. Then, the compact local integrated radial basis functions (RBFs) is used to approximate the spatial derivative. The utilized numerical method is a truly meshless technique. The numerical approach put forth is genuinely meshless, allowing for the utilization of irregular physical domains in obtaining numerical solutions.

Keywords