A new class of second order linearly implicit fractional. step methods

[摘要] A new family of linearly implicit fractional step methods is proposed and analysed in this paper. The combination of one of these time integrators with a suitable spatial discretization permits a very efficient numerical solution of semilinear parabolic problems. The main quality of this new family of methods, compared to other existing time integrators of this type, is that they are stable when the spatial differential operator is decomposed in a number in of simpler operators which do not necessarily commute. We prove that these methods satisfy this general stability result as well as they are second order consistent. Both consistency and stability are proven for an operator splitting in an arbitrary number in of terms (m >= 2). Finally, a numerical experiment illustrates these theoretical results in the last section of the paper. (c) 2008 Elsevier B.V. All rights reserved.

[发布日期] 2008-09-01

[效力级别]  Proceedings Paper

[关键词] fractional step methods;semilinear parabolic problems;stability