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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 3, Pages 405–412 (Mi zvmmf11044)  

Numerical continuation method for nonlinear system of scalar and functional equations

N. B. Melnikova, G. V. Paradezhenkoa, B. I. Reserb

a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Mikheev Institute of Metals Physics UrB RAS, Ekaterinburg, 620108 Russia

Abstract: We propose a numerical continuation method for a nonlinear system that consists of scalar and functional equations. At each parameter step, we solve the system by a modified Gauss–Seidel method. An advantage of this method is that the system is divided into two parts and each part is solved by a suitable numerical method with a desired precision. We solve the functional equations self-consistently at each step of the iteration process for the system of scalar equations. We apply the proposed method for calculating temperature dependence of magnetic characteristics of metals in the dynamic spin-fluctuation theory.

Key words: numerical continuation, nonlinear systems, Gauss–Seidel method, temperature dependence, magnetic characteristics, spin fluctuations

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation AAAA-A18-118020190098-5
18-2-2-11
This research was performed within the state assignment of the Ministry of Science and Education of Russia (Theme “Electron” no. AAAA-A18-118020190098-5) and was supported in part by a program of the Ural Branch of Russian Academy of Sciences (project no. 18-2-2-11).


DOI: https://doi.org/10.31857/S0044466920030114


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:3, 404–410

Bibliographic databases:

UDC: 519.622
Received: 01.07.2019
Revised: 02.09.2019
Accepted:18.11.2019

Citation: N. B. Melnikov, G. V. Paradezhenko, B. I. Reser, “Numerical continuation method for nonlinear system of scalar and functional equations”, Zh. Vychisl. Mat. Mat. Fiz., 60:3 (2020), 405–412; Comput. Math. Math. Phys., 60:3 (2020), 404–410

Citation in format AMSBIB
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\paper Numerical continuation method for nonlinear system of scalar and functional equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 3
\pages 405--412
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\crossref{https://doi.org/10.31857/S0044466920030114}
\elib{https://elibrary.ru/item.asp?id=42445964}
\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 3
\pages 404--410
\crossref{https://doi.org/10.1134/S0965542520030112}
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