A compact fourth-order in space energy-preserving method for Riesz space-fractional nonlinear wave equations

J.E. Macías-Díaz, A.S. Hendy and R.H. De Staelen

Applied Mathematics and Computation, 2018, vol. 325, issue C, 1-14

Abstract: In this work, we investigate numerically a nonlinear hyperbolic partial differential equation with space fractional derivatives of the Riesz type. The model under consideration generalizes various nonlinear wave equations, including the sine-Gordon and the nonlinear Klein–Gordon models. The system considered in this work is conservative when homogeneous Dirichlet boundary conditions are imposed. Motivated by this fact, we propose a finite-difference method based on fractional centered differences that is capable of preserving the discrete energy of the system. The method under consideration is a nonlinear implicit scheme which has various numerical properties. Among the most interesting numerical features, we show that the methodology is consistent of second order in time and fourth order in space. Moreover, we show that the technique is stable and convergent. Some numerical simulations show that the method is capable of preserving the energy of the discrete system. This characteristic of the technique is in obvious agreement with the properties of its continuous counterpart.

Keywords: Conservative fractional wave equation; Riesz space-fractional equations; Energy-preserving method; Fractional centered differences; High-order approximation; Stability and convergence analyses (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:325:y:2018:i:c:p:1-14

DOI: 10.1016/j.amc.2017.12.002

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