jzs-10827

Numerical investigation of the two– dimensional time–dependent diffusion equation using Radial basis functions

 Hamid Mesgarani*1, Mahya Kermani1, and Yaqub Azari1

1 Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, 16785-163

*Corresponding author’s e-mail: hmesgarani@sru.ac.ir

Original: 21 February 2020        Revised: 17 August 2020        Accepted: 26 September 2020        Published online: 20 December 2020  

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Abstract

In this paper, we investigate the numerical solution of the two–dimensional time–dependent diffusion equation with non-local and mixed Neumann–Dirichlet boundary conditions. In the discretization process, the backward Euler as well as Crank–Nicolson schemes and radial basis function (RBF) collocation method are respectively used to discretize time derivative and spatial derivative terms. The accuracy and applicability of the presented methods are illustrated and compared by solving two examples.

Key Words: Non–local boundary value problem, Diffusion equation, Kansa’s method, Radial basis functions (RBFs), Meshless method

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