Deriving a new centrodal Runge Kutta method with predictor corrector style

Jasim, Mahmood D.

doi:10.47974/JIM-1874

Open Access Research Article

Deriving a new centrodal Runge Kutta method with predictor corrector style

^*Mahmood D. JasimCorresponding authormahoodalani@uomosul.edu.iq; Mahmood.Al-Ani@univ-nantes.frDepartment of Mathematics College of Basic Education University of MosulDepartment of Mathematics College of Basic Education University of MosulMosul, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 799–805Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1874XML

Received:: 13 Dec 2023
Published Online:: 30 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1874
Pages:: 799–805

Abstract

In this research, we derived a new Runge - Kutta (RK) method with a Centrodal mean, based on the principle of guesswork and correction, to obtain a new connection for this method, where we can use its two parts at the same time (in parallel). So, it’s makes this method more suitable for multi-processor computers that exist at this time than sequential methods previous.

Keywords

Initial value problems Predictor corrector Runge kutta methods Centrodal mean Stability

Subject Classifications

32E3032E05

References

[1] Miranker, M.L. and Liniger, W., “parallel methods for numerical integration of Ordinary Differential Equations”, Journal of Mathematical Computation, Vol 21, pp. 303 – 319, (1967).
[2] Evans, D. J. and A. R. Yaakub, “A New Forth Order Runge – Kutta Formula Based on the Centroidal Mean (CoM) Formula”, Parallel Algorithms Research Centre , University of Technology, Loughbrough, Leics, U. K., report No. 849, (1993).
[3] Jasim, M. D., “Using the Centrodal Mean to Building Parallel Predictor Corrector Runge Kutta. Method”, AIP Conference Proceedings 2398, (2022), https://doi.org/10.1063/5.0093381.
[4] Jasim, M.D., “Parallel Second Order Runge – Kutta new method of the Geometric Mean”, College of Basic Education Researchers Journal Vol. 16, No. 3, pp. 944-953, (2020).
[5] Jasim, M. D., “Two new Runge Kutta methods based on the root mean square formula for folving IVPs in ODEs”, Journal of Interdisciplinary Mathematics, vol. 24, no. 7, pp, 1947–1953 (2021), doi: 10.1080/09720502.2021.1981029.
[6] Tin-Osa B. F., “A New 4th Order Hybrid Runge-Kutta Methods for Solving Initial Value Problems”, Pure and Applied Mathematics Journal, Vol. 7, No. 6, pp. 78-87 (2019).
[7] Sharmila, R. G., “Fourth Order Runge-Kutta Method Based On Geometric Mean for Hybrid Fuzzy Initial Value Problems”, IOSR Journal of Mathematics, Vol. 13, Issue 2 Ver. II, PP 43-51, (2017).
[8] Lambert J. D., “Numerical Methods for Ordinary Differential Systems, the initial value Problem”, John Wiley & Sons Ltd, (2000).
[9] Lambert J. D., “Methods for Ordinary Differential Systems: The Initial Value Problem”, McGraw- Hill; 1st edition, (2014).
[10] Agbeboh G.U., “On the Stability Analysis of a Geometric Mean 4th Order Runge - Kutta. Formula”, Mathematical Theory and Modeling, Vol.3, No.4, (2013).
[11] Anaz A. S. and, Faris D. M., “Comparison between open CV and MATLABperformance in realtime applications”, Al-Rafidain Engineering Journal (AREJ), (2015).
[12] Abbood, Mohaimen M. , Ebrahim, Hassan H., Al-Fayadh, Ali & Obaid, Ahmed J. () Measure defined on & Gamma; – algebra and some of their generalizations, Journal of Interdisciplinary Mathematics, 1-7, DOI: 10.47974/JIM-1502.
[13] Shelash, Hader Baqer, Ahmad, Hasanain Hamid & Obaid, Ahmed J. On characterizations some of subgroups of the dihedral group D2n, Journal of Discrete Mathematical Sciences and Cryptography, 1-6, DOI: 10.47974/JDMSC-1553.

Views: 131Downloads: 4Citations: 0