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Journal of Scientific Computing

Erschienen in:

28.01.2016

High Order Semi-implicit Schemes for Time Dependent Partial Differential Equations

verfasst von: Sebastiano Boscarino, Francis Filbet, Giovanni Russo

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2016

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Abstract

The main purpose of the paper is to show how to use implicit–explicit Runge–Kutta methods in a much more general context than usually found in the literature, obtaining very effective schemes for a large class of problems. This approach gives a great flexibility, and allows, in many cases the construction of simple linearly implicit schemes without any Newton’s iteration. This is obtained by identifying the (possibly linear) dependence on the unknown of the system which generates the stiffness. Only the stiff dependence is treated implicitly, then making the whole method much simpler than fully implicit ones. The resulting schemes are denoted as semi-implicit R–K. We adopt several semi-implicit R–K methods up to order three. We illustrate the effectiveness of the new approach with many applications to reaction–diffusion, convection diffusion and nonlinear diffusion system of equations.

Vorheriger Artikel A Posteriori Error Analysis of the Discontinuous Galerkin Method for Two-Dimensional Linear Hyperbolic Conservation Laws on Cartesian Grids

Nächster Artikel High Order Finite Difference Methods for the Wave Equation with Non-conforming Grid Interfaces

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Titel: High Order Semi-implicit Schemes for Time Dependent Partial Differential Equations
verfasst von: Sebastiano Boscarino
Francis Filbet
Giovanni Russo
Publikationsdatum: 28.01.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0168-y

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