Abstract

The convergence and accuracy of a method for solving high-order accurate bicompact schemes having the fourth order of approximation in spatial variables on a minimum stencil for a multidimensional inhomogeneous advection equation are investigated. The method is based on the approximate factorization of difference operators of multidimensional bicompact schemes. In addition, it uses iterations to preserve a high (higher than the second) order of accuracy of bicompact schemes in time. The convergence of these iterations for both two- and three-dimensional bicompact schemes as applied to the linear inhomogeneous advection equation with positive constant coefficients is proved using the spectral method. The efficiency of two parallel algorithms for solving equations of multidimensional bicompact schemes is compared. One of them is the spatial marching algorithm for calculating unfactorized schemes, and the other is based on iterative approximate factorization of difference operators of the schemes.

中文翻译：

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多维高精度双紧方案中算子迭代近似因式分解方法的收敛性和准确性

摘要

研究了求解多维不均匀对流方程的最小模板上具有空间变量四阶近似的高阶精确双紧方案的方法的收敛性和准确性。该方法基于多维双紧方案的差分算子的近似因式分解。另外，它使用迭代来保持双紧凑方案在时间上的高（高于第二）精度。使用频谱方法证明了将二维和紧凑双线性方案的这些迭代应用于具有正常数系数的线性不均匀对流方程的收敛性。比较了两种并行算法求解多维双紧凑型方案方程的效率。