This paper focuses on developing the reduced-order extrapolated model based on the splitting implicit finite difference (SIFD) scheme and the proper orthogonal decomposition (POD) for the two-dimensional (2D) fourth-order nonlinear Rosenau equation. For this purpose, we first construct the SIFD scheme and analyze the stability and convergence. And then, we develop a reduced-order extrapolated SIFD (ROESIFD) scheme for the Rosenau equation by POD technique and analyze the ability and convergence for the ROESIFD solutions. Finally, we enumerate an example to illustrate the efficacy and feasibility of the ROESIFD scheme.

中文翻译：

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基于分裂隐式有限差分格式和适当正交分解的四阶非线性Rosenau方程的降阶外推模型

本文重点研究基于二维隐式有限差分（SIFD）方案和二维（2D）非线性非线性Rosenau方程的适当正交分解（POD）的降阶外推模型。为此，我们首先构造SIFD方案并分析稳定性和收敛性。然后，我们通过POD技术为Rosenau方程开发了降阶外推SIFD（ROESIFD）方案，并分析了ROESIFD解的能力和收敛性。最后，我们列举一个例子来说明ROESIFD方案的有效性和可行性。