论文标题
一些二阶进化方程的分裂方案
Splitting Schemes for Some Second-Order Evolution Equations
论文作者
论文摘要
我们考虑了二阶进化方程的库奇问题，其中问题运算符是两个自伴操作员的总和。该问题的主要特征是，其中一个操作员以其共轭a*为代表。进行时间近似，以便将及时的过渡到新的水平与操作员A和A*的单独问题解决方案有关，而不是其产品。无条件稳定方案的构建基于希尔伯特空间中操作员差异方案的稳定理论（正确性）的一般结果，并且与问题运营商的乘法扰动有关，这导致了稳定的隐式方案。例如，考虑了弹性基础上薄板动力学的问题。
We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of the product of operator A by its conjugate A*. Time approximations are carried out so that the transition to a new level in time was associated with a separate solution of problems for operators A and A*, not their products. The construction of unconditionally stable schemes is based on general results of the theory of stability (correctness) of operator-difference schemes in Hilbert spaces and is associated with the multiplicative perturbation of the problem operators, which lead to stable implicit schemes. As an example, the problem of the dynamics of a thin plate on an elastic foundation is considered.
