发表机构
Ivane Javakhishvili Tbilisi State University; Ilia Vekua Institute of Applied Mathematics; The University of Georgia（伊万·贾瓦希什维利第比利斯国立大学; 伊利娅·韦库阿应用数学研究所; 格鲁吉亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究齐次抽象双曲方程柯西问题，构造与旋转矩阵相关酉算子群的有理逼近并证明其有四阶收敛性，在此基础上构建两层半离散格式求解非齐次方程柯西问题，研究格式收敛性质。
AI 中文摘要
齐次抽象双曲方程柯西问题的解及其导数，可通过与旋转矩阵相关的酉算子群进行向量表示。构造了该酉群的有理逼近，并证明其具有最优的四阶收敛性。根据光滑度尺度确定收敛阶。基于此有理逼近，构建了两层半离散格式用于求解非齐次抽象双曲方程柯西问题的近似解，研究了该格式与解的正则性相关的收敛性质。
英文摘要
The solution of the Cauchy problem for homogeneous abstract hyperbolic equations, together with its derivative, admits a vector representation in terms of a unitary operator group associated with a rotation matrix. A rational approximation of this unitary group is constructed and shown to possess optimal fourth-order convergence. The order of convergence is determined in accordance with the smoothness scale. Based on this rational approximation, a two-layer semi-discrete scheme is constructed for the approximate solution of Cauchy problems for nonhomogeneous abstract hyperbolic equations in both the linear and semilinear settings. The convergence properties of the scheme are examined in relation to the regularity of the solution.
CommentsThis is the third updated version, which incorporates changes to the Introduction and Literature Review, as well as further substantiation of certain facts. The current manuscript consists of 23 pages, including the cover page, and contains 31 references
