Numerical solution of time-dependent advection-diffusion-reaction equations

By Willem Hundsdorfer, Jan G. Verwer. 2003

1,551 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a1b151c985a70d6e7c6a2cbf78d717c0f6e87dd6

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In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

RKC time-stepping for advection-diffusion-reaction problems (2004, background): “Taking = 2/13, as in [7, 18], we get approximately 0.”
High order splitting methods for analytic semigroups exist (2009, background): “Contemporary surveys addressing the usage of exponential splitting meth ods can be found in [6,10, 11].”
Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms (2007, methodology): “This scheme has been considered in [10,11] for the application to convection–diffusion–reaction problems without mixed derivative terms.”
Error analysis of finite difference and Markov chain approximations for option pricing (2018, positive): “The discretization scheme presented above is known as the method of lines (Hundsdorfer & Verwer, 2003), in which only spatial derivatives are discretized.”
Numerical Methods for Evolutionary Differential Equations (2008, methodology): “Our main references here are LeVeque [116] and Shu [156]; see also Hundsdorfer and Verwer [98] and Hirsch [92].”
Modelling present and climate-shifted distribution of marine fishes and invertebrates. (2008, neutral): “…of pelagic larval dispersal were modelled by a two-dimensional advection-diffusion equation (e.g., Sibert et al. 1999; Gaylord & Gaines 2000; Hundsdorfer & Verwer 2003): ( ) ( ) Lav N v y Lav u x y Lav D y x Lav D x t Lav ⋅ − ⋅ ∂ ∂ − ⋅ ∂ ∂ −         ∂ ∂ ∂ ∂ +       ∂ ∂ ∂ ∂ = ∂…”
Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations (2008, background): “(See e.g.[ 14 ].) Hence, for many important classes of matrices we can prove the validity.”
Strong stability of singly-diagonally-implicit Runge--Kutta methods (2008, neutral): “where φ(θ) is a (limiter) function due to Koren – see [20] – defined by”