Abstract

Computational practice widely employs inhomogeneous time approximations in which one part of the problem operator is taken from the lower time level and the other, from the upper one. We discuss questions of constructing explicit–implicit schemes for the approximate solution of the Cauchy problem for a first-order evolution equation based on additive two-component splitting of the main problem operator. Novel explicit–implicit schemes are proposed when splitting the operator multiplying the time derivative. The stability of the proposed explicit–implicit two- and three-level operator-difference schemes is investigated.

中文翻译：

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一阶发展方程的显式-隐式格式

摘要

计算实践广泛采用非均匀时间逼近，其中问题算子的一部分取自较低的时间级别，另一部分取自较高的时间级别。我们讨论了基于主问题算子的加法二分量分裂的一阶演化方程的柯西问题的近似解的构造显式-隐式方案的问题。当拆分算子乘以时间导数时，提出了新颖的显式-隐式方案。研究了所提出的显式-隐式两级和三级算子差分方案的稳定性。