Journal Article

FZJ-2019-01365

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png ESERK5: A fifth-order extrapolated stabilized explicit Runge–Kutta method

Martín-Vaquero, J. (Corresponding author) ; Kleefeld, A.FZJ*

2019
North-Holland Amsterdam

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Please use a persistent id in citations: http://hdl.handle.net/2128/21729  doi:10.1016/j.cam.2019.01.040

Abstract: A new algorithm is developed and analyzed for multi-dimensional non-linear parabolic partial differential equations (PDEs) which are semi-discretized in the spatial variables leading to a system of ordinary differential equations (ODEs). It is based on fifth-order extrapolated stabilized explicit Runge–Kutta schemes (ESERK). They are explicit methods, and therefore it is not necessary to employ complicated software for linear or non-linear system of equations. Additionally, they have extended stability regions along the negative real semi-axis, hence they can be considered to solve stiff problems coming from very common diffusion or reaction–diffusion problems.Previously, only lower-order codes (up to fourth-order) have been constructed and made available in the scientific literature. However, at the same time, higher-order codes were demonstrated to be very efficient to solve equations where it is necessary to have a high precision or they have transient zones that are very severe, and where functions change very fast. The new schemes allow changing the step length very easily and with a very small computational cost. Thus, a variable step length, with variable number of stages algorithm is constructed and compared with good numerical results in relation to other well-known ODE solvers.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)

Appears in the scientific report 2019

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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