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Journal of Scientific Computing

Erschienen in:

14.10.2015

Fast High-Order Compact Exponential Time Differencing Runge–Kutta Methods for Second-Order Semilinear Parabolic Equations

verfasst von: Liyong Zhu, Lili Ju, Weidong Zhao

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

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Abstract

In this paper we propose fast high-order numerical methods for solving a class of second-order semilinear parabolic equations in regular domains. The proposed methods are explicit in nature, and use exponential time differencing and Runge–Kutta approximations in combination with a linear splitting technique to achieve accurate and stable time integration. A two-step compact difference scheme is employed for spatial discretization to obtain fourth-order accuracy and make use of FFT-based fast calculations. Such methods can be applied to problems with stiff nonlinearities and boundary conditions of Dirichlet or periodic types. Linear stability analysis and various numerical experiments are also presented to demonstrate accuracy and stability of the proposed methods.

Vorheriger Artikel Construction of Additive Semi-Implicit Runge–Kutta Methods with Low-Storage Requirements

Nächster Artikel Parametrized Positivity Preserving Flux Limiters for the High Order Finite Difference WENO Scheme Solving Compressible Euler Equations

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Titel: Fast High-Order Compact Exponential Time Differencing Runge–Kutta Methods for Second-Order Semilinear Parabolic Equations
verfasst von: Liyong Zhu
Lili Ju
Weidong Zhao
Publikationsdatum: 14.10.2015
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/s10915-015-0117-1

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