Paper Info
Title
Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term
Abstract
In this paper, we develop a family of second-order semi-implicit time integration methods for systems of ordinary differential equations (ODEs) with stiff damping term. The important feature of the new methods resides in the fact that they are capable of exactly preserving the steady states as well as maintaining the sign of the computed solution under the time step restriction determined by the nonstiff part of the system only. The new semi-implicit methods are based on the modification of explicit strong stability preserving Runge-Kutta (SSP-RK) methods and are proven to have a formal second order of accuracy, A(alpha)-stability, and stiff decay. We illustrate the performance of the proposed SSP-RK based semi-implicit methods on both a scalar ODE example and a system of ODEs arising from the semi-discretization of the shallow water equations with stiff friction term. The obtained numerical results clearly demonstrate that the ability of the introduced ODE solver to exactly preserve equilibria plays an important role in achieving high resolution when a coarse grid is used.
Year
DOI
Venue
2015
10.1137/151005798
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
Field
DocType
ordinary differential equations with stiff damping terms,semi-implicit methods,strong stability preserving Runge-Kutta methods,implicit-explicit methods,shallow water equations with friction terms
Numerical methods for ordinary differential equations,Runge–Kutta methods,Explicit and implicit methods,Mathematical optimization,Ordinary differential equation,Mathematical analysis,L-stability,Backward differentiation formula,Ode,Mathematics,Shallow water equations
Journal
Volume
Issue
ISSN
53
4
0036-1429
Citations 
PageRank 
References 
7
0.49
4
Authors
4
Name
Order
Citations
PageRank
Alina Chertock1102.92
Shumo Cui2110.89
Alexander Kurganov319427.02
Tong Wu412426.50