Modification of Fourth order Runge-Kutta Method for Kutta Form With Geometric Means

Authors

  • Irma Suryani UIN Sultan Syarif Kasim Riau
  • Roni Roni
  • Wartono Wartono
  • Yuslenita Muda

DOI:

https://doi.org/10.15575/kubik.v4i2.6425

Keywords:

Taylor’s series, first order differential equaton, geometric means, Fourth order Runge-Kutta method for Kutta form

Abstract

This paper  discuss how to modified Fourth order Runge-Kutta Kutta method based on the geometric mean. Then we have parameters  and   however by re-comparing the Taylor series expansion of   and  up to the 4th order.  For make error term re-compering of  the Taylor series expansion of  and  up to the 5th order. In the error term an make substitution for the values of  and  into the Taylor seriese expansion up to the 5th order. So that we have error term modified Fourth Order Runge-Kutta Kutta based on the geometric mean.  Modified Fourth Order Runge-Kutta Kutta based on the geometric mean that usually used to solved ordinary differential equations.

References

N. Thurey, T. Pohl, U. Rude, M. Ochsner, and C. Korner, “Optimization and stabilization of lbm free surface ow simulations using adaptive parametrizationâ€, Science Direct Computer and Fluids, 35:934-939, 2006

D. Nuraiman, S. Viridi, dan A. Purqon, “Visualisasi Gelombang Tsunami 2 Dimensi Menggunakan Metode Lattice-Boltzmannâ€, Prosiding Simposium Nasional Inovasi Pembelajaran dan Sains 2014 (SNIPS 2014), 10-11 Juni, Bandung, Indonesia, pp. 150-153

J. G. Zhou, “Lattice Boltzmann methods for shallow water fowsâ€, Penerbit Springer, New York, 2004, p. 20

J. B. Frandsen, “Free-surface lattice Boltzmann modeling in single phase flowsâ€, Advanced Numerical Models for Simulating Tsunami Waves and Runup, P.L.-F. Liu, H. Yeh, dan C. Synolakis (editor), Penerbit World Scientific, Singapore, 2008, p. 163

Jaka Sembung, “Kiat Membuat Pupuk Organikâ€, Trubus, Feb 2014, p. 50

N. Thurey, “Physically based animation of free surface ows with the lattice Boltzmann methodâ€, Disertasi Doktor, University of Erlangen, Nurnberg, 2007, p. 30

Joe Groff, “An intro to modern OpenGL. Chapter 1: The Graphics Pipelineâ€, http://duriansoftware.com/joe/An-intro-to-modern-OpenGL.-Chapter-1:-The-Graphics-Pipeline.html [diakses 01 Februari 2015]

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Published

2020-04-30

Issue

Vol. 4 No. 2 (2019): KUBIK : Jurnal Publikasi Ilmiah Matematika

Section

Articles

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