Uniform convergence and stability of linearized fourth-order conservative compact scheme for Benjamin-Bona-Mahony-Burgers' equation

09/26/2020
by   Qifeng Zhang, et al.
0

In the paper, a newly developed three-point fourth-order compact operator is utilized to construct an efficient compact finite difference scheme for the Benjamin-Bona-Mahony-Burgers' (BBMB) equation. Detailed derivation is carried out based on the reduction order method together with a three-level linearized technique. The conservative invariant, boundedness and unique solvability are studied at length. The uniform convergence is proved by the technical energy argument with the optimal convergence order 𝒪(τ^2+h^4) in the sense of the maximum norm. The almost unconditional stability can be achieved based on the uniform boundedness of the numerical solution. The present scheme is very efficient in practical computation since only a system of linear equations with a symmetric circulant matrix needing to be solved at each time step. The extensive numerical examples verify our theoretical results and demonstrate the superiority of the scheme when compared with state-of-the-art those in the references.

READ FULL TEXT
11/16/2019

A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

This paper aims to develop a linearly implicit structure-preserving nume...
07/21/2021

A mass-conservative Lagrange–Galerkin scheme of second order in time for convection-diffusion problems

A mass-conservative Lagrange–Galerkin scheme of second order in time for...
06/22/2020

A second order accurate numerical scheme for the porous medium equation by an energetic variational approach

The porous medium equation (PME) is a typical nonlinear degenerate parab...
01/26/2021

On Properties of Compact 4th order Finite-Difference Schemes for the Variable Coefficient Wave Equation

We consider an initial-boundary value problem for the n-dimensional wave...
12/02/2020

A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes

We study necessary conditions for stability of a Numerov-type compact hi...
08/25/2021

Fourth order compact scheme for the Navier-Stokes equations on time deformable domains

In this work, we report the development of a spatially fourth order temp...