Journal ArticleDOI
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
TLDR
Runge-Kutta-based IMEX schemes are developed that have better stability regions than the best known IMEX multistep schemes over a wide parameter range.About:
This article is published in Applied Numerical Mathematics.The article was published on 1997-11-01. It has received 1176 citations till now. The article focuses on the topics: Runge–Kutta methods & Partial differential equation.read more
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Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers.
TL;DR: The SUNDIALS suite of nonlinear and DIfferential/ALgebraic equation solvers (SUNDIALs) as mentioned in this paper has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures.
Book
Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems
TL;DR: This book discusses infinite difference approximations, Iterative methods for sparse linear systems, and zero-stability and convergence for initial value problems for ordinary differential equations.
Journal ArticleDOI
Fourth-Order Time-Stepping for Stiff PDEs
TL;DR: A modification of the exponential time-differencing fourth-order Runge--Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators.
Journal ArticleDOI
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
TL;DR: Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations and results for the fifth-order method are disappointing, but both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods.
Journal ArticleDOI
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Lorenzo Pareschi,Giovanni Russo +1 more
TL;DR: New implicit–explicit (IMEX) Runge–Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms are considered, with high accuracy in space and several applications are presented.
References
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Book
Spectral Methods in Fluid Dynamics
M. Y. Hussaini,Thomas A. Zang +1 more
TL;DR: Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.
Book
Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems
Ernst Hairer,Gerhard Wanner +1 more
TL;DR: In this paper, the authors present the solution of stiff differential equations and differential-algebraic systems (differential equations with constraints) and discuss their application in physics, chemistry, biology, control engineering, electrical network analysis, and computer programs.
Book
Solving Ordinary Differential Equations I: Nonstiff Problems
TL;DR: In this paper, the authors describe the historical development of the classical theory of linear methods for solving nonstiff ODEs and present a modern treatment of Runge-Kutta and extrapolation methods.
Journal ArticleDOI
Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations
John Kim,Parviz Moin +1 more
TL;DR: In this paper, a numerical method for computing three-dimensional, time-dependent incompressible flows is presented based on a fractional-step, or time-splitting, scheme in conjunction with the approximate-factorization technique.
Journal ArticleDOI
High-order splitting methods for the incompressible Navier-Stokes equations
TL;DR: Improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods, and a new family of stiffly stable schemes is employed in mixed explicit/implicit time-intgration rules.
Related Papers (5)
Implicit-explicit methods for time-dependent partial differential equations
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems
Ernst Hairer,Gerhard Wanner +1 more