Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation

Mojtaba Hajipour, Amin Jajarmi, Alaeddin Malek and Dumitru Baleanu

Applied Mathematics and Computation, 2018, vol. 325, issue C, 146-158

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.

Keywords: Positivity-preserving WENO scheme; Semi-implicit Runge–Kutta method; Sixth order; Nonlinear heat equation (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:325:y:2018:i:c:p:146-158

DOI: 10.1016/j.amc.2017.12.026

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