Explicit–Implicit Schemes for First-Order Evolution Equations

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.