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Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'')


Ghawadri, Nizam Ghannam Fayez and Senu, Norazak and Alshareeda, Firas Adel Fawzi and Ismail, Fudziah and Ibrahim, Zarina Bibi (2019) Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u''). Symmetry, 11 (2). art. no. 246. pp. 1-30. ISSN 2073-8994


The primary contribution of this work is to develop direct processes of explicit Runge-Kutta type (RKT) as solutions for any fourth-order ordinary differential equation (ODEs) of the structure u(4)=f(x,u,u′,u′′) and denoted as RKTF method. We presented the associated B-series and quad-colored tree theory with the aim of deriving the prerequisites of the said order. Depending on the order conditions, the method with algebraic order four with a three-stage and order five with a four-stage denoted as RKTF4 and RKTF5 are discussed, respectively. Numerical outcomes are offered to interpret the accuracy and efficacy of the new techniques via comparisons with various currently available RK techniques after converting the problems into a system of first-order ODE systems. Application of the new methods in real-life problems in ship dynamics is discussed.

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Official URL or Download Paper: https://www.mdpi.com/2073-8994/11/2/246

Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.3390/sym11020246
Publisher: MDPI
Keywords: Runge-Kutta type methods; Fourth-order ODEs; Order conditions; B-series; Quad-colored trees
Depositing User: Nabilah Mustapa
Date Deposited: 04 May 2020 17:37
Last Modified: 04 May 2020 17:37
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3390/sym11020246
URI: http://psasir.upm.edu.my/id/eprint/77861
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