High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations  

作　　者：Giacomo Albi Lorenzo Pareschi 

机构地区：[1]Computer Science Department,University of Verona,Verona 37134,Italy [2]Mathematics and Computer Science Department,University of Ferrara,Ferrara 44121,Italy

出　　处：《Communications on Applied Mathematics and Computation》2021年第4期701-718,共18页应用数学与计算数学学报（英文）

基　　金：Open Access funding provided by Universita degli Studi di Verona.

摘　　要：We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form,typically used in implicit-explicit(IMEX)methods,is not possible.As shown in Boscarino et al.(J.Sci.Comput.68:975-1001,2016)for Runge-Kutta methods,these semi-implicit techniques give a great flexibility,and allow,in many cases,the construction of simple linearly implicit schemes with no need of iterative solvers.In this work,we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype lineal'advection-diffusion equation and in the setting of strong stability preserving(SSP)methods.Our findings are demonstrated on several examples,including nonlinear reaction-diffusion and convection-diffusion problems.

关 键 词：Semi-implicit methods Implicit-explicit methods Multistep methods Strong stability preserving High order accuracy 

分 类 号：O17[理学—数学]