Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8901161 | Applied Mathematics and Computation | 2018 | 13 Pages |
Abstract
This paper presents a class of semi-implicit finite difference weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear heat equation. For the discretization of second-order spatial derivatives, a sixth-order modified WENO scheme is directly implemented. This scheme preserves the positivity principle and rejects spurious oscillations close to non-smooth points. In order to admit large time steps, a class of implicit Runge-Kutta methods is used for the temporal discretization. The implicit parts of these methods are linearized in time by using the local Taylor expansion of the flux. The stability analysis of the semi-implicit WENO scheme with 3-stages form is provided. Finally, some comparative results for one-, two- and three-dimensional PDEs are included to illustrate the effectiveness of the proposed approach.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Mojtaba Hajipour, Amin Jajarmi, Alaeddin Malek, Dumitru Baleanu,