Numerical investigation of the two– dimensional time–dependent diffusion equation using Radial basis functions - Mesgarani, Hamid; Kermani, Mahya; Azari, Yaqub (Sulaimani Journal for Pure and Applied Sciences, 2020)
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.
Keywords: Non–local boundary value problem; Diffusion equation; Kansa’s method; Radial basis functions (RBFs); Meshless method