An efficient local meshless approach for solving nonlinear time-fractional fourth-order diffusion model

• Main Authors: O. Nikan, Z. Avazzadeh, J.A. Tenreiro Machado
• Format: Article
• Language: English
• Published: Elsevier 2021-01-01
• Series: Journal of King Saud University: Science
• Subjects: Nonlinear time-fractional fourth-order diffusion problem; Radial basis function; Finite difference scheme; Convergence and stability
• Online Access: http://www.sciencedirect.com/science/article/pii/S1018364720303578

This paper adopts an efficient meshless approach for approximating the nonlinear fractional fourth-order diffusion model described in the Riemann–Liouville sense. A second-order difference technique is applied to discretize temporal derivatives, while the radial basis function meshless generated the finite difference scheme approximates the spatial derivatives. One key advantage of the local collocation method is the approximation of the derivatives via the finite difference formulation, for each local-support domain, by deriving the basis functions expansion. Another advantage of this method is that it can be applied in problems with non-regular geometrical domains. For the proposed time discretization, the unconditional stability is examined and an error bound is obtained. Numerical results illustrate the applicability and validity of the scheme and confirm the theoretical formulation.