Solving Ordinary Differential Equation Using Parallel Fourth Order Runge-Kutta Method With Three Processors

Authors

  • Iman Al Fajri Hasanuddin University
  • Hendra Mesra Faculty of Mathematics and Natural Science in Hasanuddin University
  • Jeffry Kusuma Faculty of Mathematics and Natural Science in Hasanuddin University

DOI:

https://doi.org/10.20956/j.v17i3.12490

Keywords:

Fourth Order Runge-Kutta Method, Parallel Algorithm, Sequential Algorithm

Abstract

This paper presents a derivation of the Runge-Kutta or fourth method with six stages suitable for parallel implementation. Development of a parallel model based on the sparsity structure of the fourth type Runge-Kutta which is divided into three processors. The calculation of the parallel computation model and the sequential model from the accurate side shows that the sequential model is better. However, generally, the parallel method will end the analytic solution by increasing the number of iterations. In terms of execution time, parallel method has advantages over sequential method.

Downloads

Download data is not yet available.

References

Axelsson, O, dan Neytcheva, M. 2020. Numerical Solution Methods for Implicit Runge-Kutta Methods of Arbitrarily High Order. In: Proceedings of the conference 'Algoritmy 2020' Vydavateľstvo SPEKTRUM, Slovak University of Technology in Bratislava, Vol. 7, pp. 11-20

Butcher, J.C. 2008. Numericals Methods for Ordinary Differential Equations Second Edition. Wiley : USA

Cui, W., Li, Y., dan Sun, Z. 2019. A Parallel Computer Numerical Simulation Method Based on Coincident Coefficients. J. Phys.: Conf. Ser. 1486 042038

Din, U.K.S., dan Ismail, F. 2011. Parallel Two-Processor Fifth Order Diagonally Implicit Runge-Kutta Method. Menemui Matematik, Vol. 33, No. 1 : 23

Hatten, N. dan Russell, R. P. 2017. Parallel Implicit Runge-Kutta Methods Applied to Coupled Orbit/Attitude Propagation. Journal of the Astronautical Sciences, vol. 64, no. 4, pp. 333–360

Iserles, A. dan Nørsett, S. P. 1990. On the Theory of Parallel Runge-Kutta Methods. IMA J. Numer. Anal., vol. 10, no. 4, pp. 463–488

Kennedy, C.A., dan Carpenter, M.H. 2016. Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. NASA : Virginia

Maya, Rippi. 2014. Diktat Kuliah Persamaan Diferensial Biasa Revisi Keenam. IKIP Siliwangi : Bandung

Pazner, W., dan Persson, P.2017. Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations. Journal of Computational Physics, Vol. 335

Séka, H. dan Kouassi, A. R. 2019. A New Seventh Order Runge-kutta Family: Comparison with the Method of Butcher and Presentation of a Calculation Software. Math. Comput. Sci., vol. 4, no. 3, p. 68

Downloads

Published

2021-05-12

How to Cite

Fajri, I. A. ., Mesra, H., & Kusuma, J. . (2021). Solving Ordinary Differential Equation Using Parallel Fourth Order Runge-Kutta Method With Three Processors. Jurnal Matematika, Statistika Dan Komputasi, 17(3), 349-356. https://doi.org/10.20956/j.v17i3.12490

Issue

Section

Research Articles

Most read articles by the same author(s)

1 2 > >>