Implementations of Open and Closed Method Numerically: A Non-linear Equations Solution Convergence Test
DOI:
https://doi.org/10.31764/ijeca.v2i2.2041Abstract
Non-linear equations are one of the studies in mathematics. Root search in complex non-linear equations can be solved by numerical methods. Many methods to solve the equation. Therefore, the purpose of this research is to conduct simulation of closed and open methods such as Newton Raphson method, Secant method, Regula Falsi, Fixet Point, and Bisection. This is done as a form of comparative research to see the accuracy, number of iterations, and errors of each method in resolving the non-linear equations. As for the case being resolved is the roots of the exponential equation, trigonometry, logarithmic and polynomial degrees of three. The results of this study resulted in different levels of convergence in resolving each caseReferences
Bisconti, L., & Franca, M. (2015). On a non-homogeneous and non-linear heat equation. Dynamics of Partial Differential Equations, 12(4), 289–320. https://doi.org/10.4310/DPDE.2015.v12.n4.a1
Dedieu, J.-P. (2015). Newton-Raphson Method. In Encyclopedia of Applied and Computational Mathematics (pp. 1023–1028). https://doi.org/10.1007/978-3-540-70529-1_374
El-Abd, E. M. (2010). On the existence of solutions for non-linear functional integral equation. Filomat, 24(4), 17–23. https://doi.org/10.2298/FIL1004017A
Mao, J., Wei, W., & Huang, W. (2010). Nonlinear numerical method for stiff systems. ICCASM 2010 - 2010 International Conference on Computer Application and System Modeling, Proceedings, 6. https://doi.org/10.1109/ICCASM.2010.5620710
Negara, H. R. P., Syaharuddin, Kurniawati, K. R. A., & Negara, H. R. P. (2019). Analysis Of Nonlinear Models For The Acceleration Of Increasing HDI In Asia. International Journal Of Scientific & Technology Research, 8(1), 60–62.
Ratu, H., Negara, P., Mandailina, V., & Sucipto, L. (2017). Calculus Problem Solution And Simulation Using GUI Of Matlab. International Journal of Scientific & Technology Research, 6(09), 275–279.
Trofimov, V. A., & Trykin, E. M. (2014). Combined method for solving of 1d nonlinear schrödinger equation. Lecture Notes in Electrical Engineering, 307, 173–188. https://doi.org/10.1007/978-3-319-03967-1_14
Van Hecke, T. (2011). On halley’s correction to the newton-raphson method. Mathematical Scientist, 36(1), 37–42.
Downloads
Published
Issue
Section
License
In submitting the manuscript to the journal, the authors certify that:
- Authors are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal. Please also carefully read Publication Ethics
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- Authors secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- Authors agree to the following copyright agreement.
Authors who publish with IJECA (International Journal of Education and Curriculum Application) agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.Â
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.