Low storage explicit Runge-Kutta method

Diomar Cesar Lobão

doi:10.5433/1679-0375.2019v40n2p123

Low storage explicit Runge-Kutta method

Authors

Diomar Cesar Lobão Universidade Federal Fluminense - UFF/EEIMVR http://orcid.org/0000-0003-2454-2747

DOI:

https://doi.org/10.5433/1679-0375.2019v40n2p123

Keywords:

LSERK, Explicit method, Runge-Kutta, System of ODE

Abstract

This paper we are dealing with the high order accurate low storage explicit Runge Kutta (LSERK) methods which mainly are used for temporal discretization and are stable regardless of its accuracy. The main objective of this paper is to compare traditional RK with different forms of LSERK methods. The numerical experiments indicate that such methods are highly accurate and effective for numerical purposes. It’s also shown the CPU time consuming and its solution implications. The method is well suited to achieve high order accurate solution for the scalar second order IVP (Initial Value Problem) problem as it is discussed in the present paper.

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Author Biography

Diomar Cesar Lobão, Universidade Federal Fluminense - UFF/EEIMVR

PhD in Aerospace Engineering - University of Bristol. Adjunct Professor at the Universidade Federal Fluminense

References

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BUTCHER J. C. The Numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods. New York: Wiley-Interscience, 1987.

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CARPENTER, M. H.; KENNEDY C. A. Fourth-order 2N-storage Runge-Kutta schemes. NASA Technical Memorandum, Hampton, n. 109112, 1994.

KETCHESON, D. I. Runge-kutta methods with minimum storage implementations. Journal of Computational Physics, Orlando, v. 229, n. 5, p. 1763 – 1773, 2010.

NIEGEMANN, J.; DIEHL, R.; BUSCH, K. Efficient low-storage Runge–Kutta schemes with optimized stability
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WILLIAMSON, J. H. Low-storage Runge-Kutta schemes. Journal of Computational Physics, Orlando, v. 35, n. 1, p. 48–56, 1980.

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Published

2019-12-18

How to Cite

Lobão, D. C. (2019). Low storage explicit Runge-Kutta method. Semina: Ciências Exatas E Tecnológicas, 40(2), 123–128. https://doi.org/10.5433/1679-0375.2019v40n2p123

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Issue

Vol. 40 No. 2 (2019)

Section

Original Article

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