Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

By Christopher A. Kennedy, Mark H. Carpenter. 2003

829 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ad463b85089ac66ae41dad57e06523403acb11e6

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Semi-implicit spectral deferred correction methods for ordinary differential equations (2003, methodology): “To enable a direct comparison with the Additive R-K methods in [22] (hereafter ARK), the initial conditions are set to y1(0) = 2, y2(0) = −0.”
Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers (2020, methodology): “(IMEX) additive Runge-Kutta methods [6, 7, 50, 51] with the general form”
Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation (2010, neutral): “Higher order conditions can be derived as well using a generalization of Butcher 1-trees to 2-trees, see [11].”
Implicit–Explicit Multistep Methods for Fast-Wave–Slow-Wave Problems (2012, methodology): “The starting stages (one or two in the case of two-step and three-step methods, respectively) are computed using the third-order IMEX additive Runge–Kutta method of Kennedy and Carpenter (2003).”
IMEX Runge-Kutta schemes for reaction-diffusion equations (2008, background): “8) Several authors [1,3,8,13] have already studied properties of IMEX Runge–Kutta schemes for PDEs.”
Numerical methods for kinetic equations* (2014, methodology): “We refer to Ascher et al. (1997), Kennedy and Carpenter (2003) and Pareschi and Russo (2005) for details.”
Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations (2009, methodology): “Following the work [5, 65], the ARK methods are used to solve equation (6.”
On an accurate third order implicit-explicit Runge--Kutta method for stiff problems (2009, methodology): “Instead, for a detail account of the classical order conditions for IMEX R-K methods see, for example [7,20].”
Exploiting ISAT to solve the reaction–diffusion equation (2004, methodology): “Finally, Kennedy and Carpenter (2003) have examined the use of an additive Runge–Kutta scheme for convection–diffusion–reaction equations.”
High-order multi-implicit spectral deferred correction methods for problems of reactive flow (2003, methodology): “It should be noted that in [14], the ARK methods are applied to reacting flow problems in which the magnitude of the diffusion is sufficiently small that it can be treated explicitly with the advection.”
Implications of the Choice of Quadrature Nodes for Picard Integral Deferred Corrections Methods for Ordinary Differential Equations (2005, methodology): “For comparison, the test above is repeated using the ARK4(3)6L[2]SA scheme from [19].”
VARIABLE STEP-SIZE IMPLICIT-EXPLICIT LINEAR MULTISTEP METHODS FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS * (2008, methodology): “, [2, 3, 9] for further details on these powerful techniques.”
Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems (2006, methodology): “High-order localized time-integration techniques, in particular based on recently developed additive Runge-Kutta methods [21], are now available [3].”