AN EXTENSION OF PARAMETER CONTINUATION METHOD FOR SOLVING PERTURBED SYSTEMS OF NONLINEAR EQUATIONS
DOI:
https://doi.org/10.51453/2354-1431/2022/763Keywords:
Parameter continuation method, Perturbed systems of nonlinear equations, Approximate solutioAbstract
In this paper, we propose an extension of parameter continuation method for solving perturbed systems of nonlinear equations. The existence and uniqueness of the solution will be investigated. We also discuss error analysis of the method. The validity and applicability of the method is verified by an example.
Downloads
References
[1] Aslam Noor, M., Waseem, M. (2009). Some it- erative methods for solving a system of nonlin- ear equations, Comput. Math. Appl. 57: 101 - 106.
[2] Bernstein, S. N. (1906). Sur la généralisation du problème de Dirichlet, Math. Ann. 62: 253 - 271.
[3] Binh, N. T., Ninh, K. V. (2019). Parame- ter continuation method for solving nonlinear Fredholm integral equations of the second kind, Bull. Malays. Math. Sci. Soc. 42(6): 3379 - 3407.
[4] Binh, N. T. (2019). Parameter continuation method for solving systems of nonlinear equa- tions, Hanoi Pedagogical University 2 J. Sci. 63: 3–13.
[5] Binh, N. T. (2021). A new extension of param- eter continuation method for solving operator equations of the second kind, Tan Trao Univer- sity J. Sci. 21: 157 - 165.
[6] Chuong, N. M., Khai, N.V., Ninh, K.V., Tuan, N.V., Tuong, N. (2000). Numerical analysis, VietNam Education Publishing House, Hanoi.
[7] Gaponenko, Y. L. (1986). The parameter - ex- tension method for an equation of the second kind with a Lipschitz - continuous and mono- tonic operator, Comput. Maths. Math. Phys. 26(8): 1123 - 1131.
[8] Ghane-Kanafi, A., Kordrostami, S. (2016). A New Approach for Solving Nonlinear Equa- tions by Using of Integer Nonlinear Program- ming , Appl. Math. 7: 473 - 481.
[9] Leray, J., Schauder, J. (1934). Topologie et équations fonctionnelles, Ann. Ec. Norm. Sup. 51: 45 - 78.
[10] Ninh, K. V. (1999). Approximate solutions of the equation of a second kind with sum of two operators, Proc. Inst. Math. Mech. Azerb. Acad. Sci. V(X): 97 - 101.
[11] Ninh, K. V. (2011). A method of extending by parameter for approximate solutions of operator equations, Acta. Math. Vietnam. 36(1): 119 - 127.
[12] Ninh, K. V., Binh, N. T. (2019). Analytical so- lution of Volterra–Fredholm integral equations using hybrid of the Method of contractive map- ping and Parameter continuation method, Int. J. Appl. Comput. Math. 5(76): 1 - 20.
[13] Ortega, J. M., Rheinboldt, W. C. (1970). Iter- ative solution of nonlinear equations in several variables, Academic Press, New York.
[14] Trenogin, V. A. (1980). Functional Analysis, Nauka, Moscow.
[15] Trenogin, V. A.(1996). Locally invertible op- erator and parameter continuation method. Funktsional, Anal. i Prilozhen. 30(2): 93 - 95.
[16] Trenogin, V. A. (1996). Global invertibility of nonlinear operator and the method of continu- ation with respect to a parameter, Dokl. Akad. Nauk. 350(4): 1 - 3.
[17] Trenogin, V. A. (1998). Invertibility of non- linear operators and parameter continuation method (English summary). Spectral and scat- tering theory, Edited by Alexander G. Ramm, Plenum Press, New York.
[18] Vetekha, V. G.(2000). Parameter continua- tion method for ordinary differential equa- tions, Proceedings of the 2nd ISAAC Congress, Vol.1, Fukuoka, Japan, August 16 - 21.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All articles published in SJTTU are licensed under a Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA) license. This means anyone is free to copy, transform, or redistribute articles for any lawful purpose in any medium, provided they give appropriate attribution to the original author(s) and SJTTU, link to the license, indicate if changes were made, and redistribute any derivative work under the same license.
Copyright on articles is retained by the respective author(s), without restrictions. A non-exclusive license is granted to SJTTU to publish the article and identify itself as its original publisher, along with the commercial right to include the article in a hardcopy issue for sale to libraries and individuals.
Although the conditions of the CC BY-SA license don't apply to authors (as the copyright holder of your article, you have no restrictions on your rights), by submitting to SJTTU, authors recognize the rights of readers, and must grant any third party the right to use their article to the extent provided by the license.