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(τ² + h²). 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(τ² + h²) 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.

中文翻译：

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Benjamin–Bona–Mahony–Burgers方程两个线性差分格式的数值分析

在本文中，针对Benjamin-Bona-Mahony-Burgers（BBMB）方程，提出了两种线性化的有限差分方案并进行了分析。对于两电平方案的结构中，非线性项经由平均线性ķ和ķ  + 1楼中，我们证明独特有解和与会聚为了详细数值解的收敛Ô（τ ²  +  ħ ²）。对于三级线性化方案，利用外推技术将基于ψ函数的非线性项线性化。我们获得具有收敛阶数O的数值解的守恒，有界性，唯一可解性和收敛性（τ ²  +  ħ ²）在长度。此外，考虑将我们的工作扩展到带有非线性源项的BBMB方程，并插入牛顿线性化方法来处理它。数值实验证明了两种方案的适用性和准确性。