ON THE CONSISTENCY AND CONVERGENCE ANALYSIS OF A DERIVED EXPLICIT FOURTH-STAGE FOURTH-ORDER RUNGE-KUTTA METHOD

Authors

  • Esekhaigbe Aigbedion Christopher Department of Mathematics, Aduvie Pre-University College, Jahi, Abuja, Nigeria.
  • Daniel Aitusi Department of Statistics, Federal Polytechnic, Auchi, Edo State, Nigeria

DOI:

https://doi.org/10.53555/nnms.v9i8.1226

Keywords:

Consistency, Convergence, Explicit, Runge-Kutta Methods, Linear and non- linear equations, Taylor series, Parameters, Initial-value Problems, Implementation, Curve

Abstract

This paper is aimed at analyzing the consistency and convergence of a derived explicit fourth-stage fourth-order Runge-Kutta method. The analysis revealed that the method is consistent and convergent. The implementation of this method on initial-value problems was done in previous paper, and it revealed that the method compared favorably well with the existing classical fourth stage fourth order explicit Runge Kutta method

References

Agbeboh; G.U (2013) “On the Stability Analysis of a Geometric 4th order Runge–Kutta Formula”.(Mathematical Theory and Modeling ISSN 2224 – 5804 (Paper) ISSN 2225 – 0522 (Online) Vol. 3, (4)) www.iiste.org.the international institute for science, technology and education, (IISTE).

Agbeboh, G.U and Ehiemua, M (2014): Modified Kutta’s Algorithm, JNAMP, Vol. 28(1), 103 – 114.

Agbeboh, G.U and Esekhaigbe, A.C (2015); “On The Component Analysis And Transformation Of An Explicit Fourth-Stage Fourth-Order Runge-Kutta Methods”, Journal Of Natural Sciences Research ( WWW.IISTE.ORG), ISSN 2224-3186 (paper), ISSN 2225-0921 (online), Vol. 5, No. 20, 2015.

Agbeboh, G.U., (2006); “Comparison of some one – step integrators for solving singular initial value problems”, Ph. D thesis, A.A.U., Ekpoma.

Agbeboh, G.U and Aashikpelokhai, U.S.U (2007): An Analysis of order Thirteen Rational Integrator, Journal of Sc. Engr. Tech, Vol. 9(2), 4128 – 4145.

Agbeboh, G.U., Ukpebor, L.A. and Esekhaigbe, A.C., (2009); “A modified sixth stage fourth – order Runge-kutta method for solving initial – value problems in ordinary differential equations”, journal of mathematical sciences, Vol2.

Thomas, H. C, Charles, E. L, Ronald, L. R and Clifford, S (2001), “Representing Rooted Trees,” MIT Press and Mc Graw-Hill, ISBN 0-262-03293-7, PP 214-217.

Turker A. (1980)., “Applied Combinatorics” Wiley, New York.

Van der Houwen, P. J., Sommeijer, B. P., (2013a); “Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method”, Journal of mathematics problems in Engineering 1-10.

Van der Houwen, P. J., Sommeijer, B. P., (2013b); “New optimized explicit modified RKN methods for the numerical solution of the Schrodinger equation”, Journal of mathematical chemistry, 51, 390-411.

Van der Houwen, P. J., Sommeijer, B. P., (2014a); “ Runge-Kutta type methods with special properties for the numerical integration or ordinary differential equations”, physics reports, 536: 75-146.

Van der Houwen, P. J., Sommeijer, B. P., (2014b);“ Explicit multi-frequency symmetric extended RKN integrators for solving multi- frequency and multi-dimensional oscillatory reversible systems”, Calco.

Van der Houwen, P. J., Sommeijer, B. P., (2015); “Runge-Kutta projection methods with low dispersion and dissipation errors”, Advances in computational methods, 41: 231-251.

William W. (2002), “General linear methods with inherent Runge-Kutta stability”, A thesis submitted for the degree of doctor of philosophy of the University of Auckland.

Yakubu, D.G, (2010); “Uniform Accurate Order Five Radau –Runge-Kutta Collocation Methods” J. Math. Assoc. Niger. 37(2):75-94.

Published

2022-08-22

How to Cite

Christopher, E. A. ., & Aitusi, D. . (2022). ON THE CONSISTENCY AND CONVERGENCE ANALYSIS OF A DERIVED EXPLICIT FOURTH-STAGE FOURTH-ORDER RUNGE-KUTTA METHOD. Journal of Advance Research in Mathematics and Statistics (ISSN 2208-2409), 9(8), 8-17. https://doi.org/10.53555/nnms.v9i8.1226

Similar Articles

1-10 of 16

You may also start an advanced similarity search for this article.