Method of the Nonlinear Monotonic Tangent in the Solution of Transcendental Equations

The method of a curvilinear monotonic tangent in solving transcendental equations is proposed. In the denominator of the nonlinear term of the expression for the mentioned tangent, a regulating relation, which is a straight line with a control parameter, is used. An algorithm for solving the problem...

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Published in:	Mathematical models and computer simulations Vol. 15; no. 4; pp. 698 - 706
Main Author:	Lipanov, A. M.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-08-2023 Springer Nature B.V
Subjects:	Algorithms Mathematical analysis Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Simulation and Modeling Straight lines numerical solution control parameter monotonicity nonlinear tangent transcendental equation
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Abstract	The method of a curvilinear monotonic tangent in solving transcendental equations is proposed. In the denominator of the nonlinear term of the expression for the mentioned tangent, a regulating relation, which is a straight line with a control parameter, is used. An algorithm for solving the problem is described. Three examples of solving transcendental equations are performed. The efficiency of using the proposed method is shown.
AbstractList	The method of a curvilinear monotonic tangent in solving transcendental equations is proposed. In the denominator of the nonlinear term of the expression for the mentioned tangent, a regulating relation, which is a straight line with a control parameter, is used. An algorithm for solving the problem is described. Three examples of solving transcendental equations are performed. The efficiency of using the proposed method is shown.
Author	Lipanov, A. M.
Author_xml	– sequence: 1 givenname: A. M. surname: Lipanov fullname: Lipanov, A. M. email: aml35@yandex.ru organization: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
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Cites_doi	10.1007/978-94-011-3776-8
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Copyright	Pleiades Publishing, Ltd. 2023. ISSN 2070-0482, Mathematical Models and Computer Simulations, 2023, Vol. 15, No. 4, pp. 698–706. © Pleiades Publishing, Ltd., 2023. Russian Text © The Author(s), 2023, published in Matematicheskoe Modelirovanie, 2023, Vol. 35, No. 2, pp. 3–14.
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References	LipanovA. M.The multiparametric trajectory method for solving systems of functional equationsDokl. Akad. Nauk19953431531551354278 G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice Hall, Englewood Cliffs, NJ, 1977). E. I. Grigolyuk and V. I. Shalashilin, Problems of Nonlinear Deformation: The Continuation Method Applied to Nonlinear Problems in Solid Mechanics (Nauka, Moscow, 1988; Springer, Dordrecht, 1991). https://doi.org/10.1007/978-94-011-3776-8 BronshteinI. N.SemendyaevK. A.Handbook of Mathematics1986MoscowNauka VoskoboinikovYu. E.OchkovV. F.Programming and Solving Problems in Mathcad2002NovosibirskNovosib. Gos. Arkhit.-Stroit. Univ. 4468_CR4 Yu. E. Voskoboinikov (4468_CR5) 2002 A. M. Lipanov (4468_CR2) 1995; 343 I. N. Bronshtein (4468_CR3) 1986 4468_CR1
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SubjectTerms	Algorithms Mathematical analysis Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Simulation and Modeling Straight lines
Title	Method of the Nonlinear Monotonic Tangent in the Solution of Transcendental Equations
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