The numerical analysis of two linearized difference schemes for the Benjamin–Bona–Mahony–Burgers equation. Issue 6 (21st July 2020)

• Record Type: Journal Article
• Authors: Zhang, Qifeng; Liu, Lingling; Zhang, Jiyuan
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 6(2020)
• Page Start: 1790
• Page End: 1810
• Publication Date: 2020-07-21
• Subjects: Benjamin–Bona–Mahony–Burgers equation -- convergence -- linearized difference scheme; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22504
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: In the article, two linearized finite difference schemes are proposed and analyzed for the Benjamin–Bona–Mahony–Burgers (BBMB) equation. For the construction of the two‐level scheme, the nonlinear term is linearized via averaging k and k + 1 floor, we prove unique solvability and convergence of numerical solutions in detail with the convergence order O ( τ 2 + h 2 ). For the three‐level linearized scheme, the extrapolation technique is utilized to linearize the nonlinear term based on ψ function. We obtain the conservation, boundedness, unique solvability and convergence of numerical solutions with the convergence order O ( τ 2 + h 2 ) at length. Furthermore, extending our work to the BBMB equation with the nonlinear source term is considered and a Newton linearized method is inserted to deal with it. The applicability and accuracy of both schemes are demonstrated by numerical experiments.