论文标题
针对非平稳问题的分裂方案，具有合理近似值的操作员分数近似值
Splitting Schemes for Non-Stationary Problems with a Rational Approximation for Fractional Powers of the Operator
论文作者
论文摘要
讨论了凯奇问题的数值解决方案的问题。研究中问题的一个基本特征是方程包括自我伴侣正运算符的分数。在计算实践中，分数功率运算符的合理近似被广泛用于各种版本。这项工作的目的是在及时到达新水平的及时构建特殊近似值，为操作员提供了一组标准问题，而不是针对分数功率运算符。提出了具有权重参数的稳定分裂方案，以用于分数功率运算符的有理近似的加成表示。注意到将类似时间近似用于其他问题的可能性。还提出了二维非平稳问题的数值解决方案，该解决方案还提出了拉普拉斯操作员的分数功率。
Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the self-adjoint positive operator. In computational practice, rational approximations of the fractional power operator are widely used in various versions. The purpose of this work is to construct special approximations in time when the transition to a new level in time provided a set of standard problems for the operator and not for the fractional power operator. Stable splitting schemes with weights parameters are proposed for the additive representation of rational approximation for a fractional power operator. Possibilities of using similar time approximations for other problems are noted. The numerical solution of a two-dimensional non-stationary problem with a fractional power of the Laplace operator is also presented.
