In this paper we study the numerical approximation of the solution of a Cauchy problem for a first-order-in-time differential equation involving a fractional power of a self-adjoint positive operator. One popular approach for the approximation of fractional powers of such operators is based on rational approximations. The purpose of this work is to construct special approximations in time so that the solution at a new time level is produced by solving a set of standard problems involving the self-adjoint positive operator rather than its fractional power. Stable splitting schemes with weight parameters are proposed for the additive representation of the rational approximation of the fractional power of the operator. Finally, numerical results for a two-dimensional non-stationary problem with a fractional power of the Laplace operator are also presented.

在本文中，我们研究了涉及自伴正算子的分数幂的一阶时间微分方程的柯西问题解的数值近似。此类算子的分数幂近似的一种流行方法是基于有理逼近。这项工作的目的是构造特殊的时间近似值，以便通过解决一组涉及自伴正算子而不是其分数幂的标准问题来产生新时间级别的解。提出了具有权重参数的稳定拆分方案，用于对算符的分数幂进行有理逼近的加法表示。最后，