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Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation

Journal Article · · Mathematics of Computation
DOI:https://doi.org/10.1090/mcom/3967· OSTI ID:2338059
 [1];  [2]
  1. Univ. of Washington, Seattle, WA (United States); Michigan State University
  2. Univ. of Georgia, Athens, GA (United States)
+ Show Author Affiliations
Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter. Here, in this work, we prove rigorously the uniform stability and uniform accuracy of a class of IMEX-RK schemes for a linear hyperbolic system with stiff relaxation. The result we obtain is optimal in the sense that it holds regardless of the value of and the order of accuracy is the same as the design order of the original scheme, i.e., there is no order reduction.
Research Organization:
Michigan State Univ., East Lansing, MI (United States); Univ. of Georgia, Athens, GA (United States); Univ. of Washington, Seattle, WA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0023164
OSTI ID:
2338059
Journal Information:
Mathematics of Computation, Journal Name: Mathematics of Computation Vol. 94; ISSN 0025-5718
Publisher:
American Mathematical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (16)

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On an accurate third order implicit-explicit Runge–Kutta method for stiff problems journal July 2009
Asymptotic-preserving schemes for multiscale physical problems journal May 2022
On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations journal November 2020
Error Analysis of IMEX Runge–Kutta Methods Derived from Differential-Algebraic Systems journal January 2007
Implicit-Explicit Methods for Time-Dependent Partial Differential Equations journal June 1995
On a Class of Uniformly Accurate IMEX Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation journal January 2009
Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit journal January 2013
Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations journal January 2013
Implicit-Explicit Linear Multistep Methods for Stiff Kinetic Equations journal January 2017
Implicit-Explicit Multistep Methods for Hyperbolic Systems With Multiscale Relaxation journal January 2020
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations journal January 1999

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Related Subjects

97 MATHEMATICS AND COMPUTING
energy estimate
hyperbolic relaxation system
implicit-explicit Runge-Kutta method
stiff