THE DERIVED EXPLICIT FOURTH-STAGE SECOND-ORDER RUNGE-KUTTA METHOD IS CONSISTENT AND CONVERGENT
DOI:
https://doi.org/10.53555/nnms.v10i2.1519Keywords:
Consistency, Convergence, Explicit, Runge-Kutta Methods, Linear and non- linear equations, Taylor series, Parameters, Initial-value ProblemsAbstract
The purpose of this paper is to analyze the consistency and convergence of an explicit fourth-stage second-order Runge-Kutta method derived using Taylor series expansion by varying parameters. The analysis revealed that the method is consistent and convergent. These properties are key and vital for any numerical method to possess for it to be capable of handling initial value problems. The implementation of this method on initial-value problems has been done in previous paper, and it revealed that the method compared favorably well with the other existing explicit Runge Kutta method of the same order. Hence, as a result of the convergence and consistency of the method, it will definitely be reliable and dependable.
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.
Barletti, L, Brugnano, L, and Yifa, T., (2020): “Spectrally accurate space time solution of manakov systems”, Mathematics, J. Comput. Appl. Math 2020.
Brugnano, L, Gurion, G, and Yadian, S., (2019): “Energy conserving Hamiltian Boundary value methods for numerical solution of korteweg de vries equations”, Mathematics, J Compt. Apll. Math. 2019.
Gianluca, F, Lavermero, F, and Vespri, V., (2021): “A new frame work for approximating differential equations”, Mathematics, Computer Science, 2021.
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., (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.
.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Journal of Advance Research in Mathematics And Statistics
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Terms & Condition
Submission -
Author can submit the manuscript through our online submission process or email us at the designated email id in contact details.
The other mode of submission not accepted than online and email.
Before submission please read the submission guidelines.
NN Publication accepts only article submitted in pdf/doc/docx/rtf file format. Another format except given file formats will no be considered .
Author will be responsible for the error mistakes in the submission files. The minor changes can be done without any cost after publication. But for major changes NN Publication may charges you the editing charges.
Publication (Online) -
The online publication is scheduled on last date of every month, but it can be delayed by 24 to 48 hours due to editorial process if huge number of articles comes to publish in single issue.
Automatic notificatation email will be sent to the all users on publication of an issue, so its author’s duty to check their email inbox or SPAM folder to get this notification.
After publication of article author can not withdraw their article.
If editor’s found any issue after publication of article then the NN Publication have the authority to remove the article from online website.
No refund will be provided after online publication of article.
Publication (Print) -
The print copy publication are sent as per the author’s request after 2 weeks of online publication of that issue.
NN Publication will ship the article by India Post and provide the consignment number on dispatch of print copy.
NN Publication follows all the guidelines of delivery provided by IndiaPost and hence not responsible for delay in delivery due to any kind of reasons.
Refund of hard copy will not be provided after dispatch or print of the journal.
NN Publication will be responsible for raise a complain if there is any issue occurs in delivery, but still will not be responsible for providing the refund.
NN Publication will be responsible to resend the print copy only and only if the print copy is lost or print copy is damaged in delivery / or there is delay more than 6 months.
According to India Post the delivery should be completed with in 1-3 weeks after dispatch of articles.
Privacy Policy-
NN Publicationl uses the email ids of authors and editors and readers for sending editorial or publication notification only, we do not reveal or sell the email ids to any other website or company.
