×

First-order methods with extended stability regions for solving electric circuit problems. (English) Zbl 07334087

Summary: Stability control of Runge-Kutta numerical schemes is studied to increase efficiency of integrating stiff problems. The implementation of the algorithm to determine coefficients of stability polynomials with the use of the GMP library is presented. Shape and size of the stability region of a method can be preassigned using proposed algorithm. Sets of first-order methods with extended stability domains are built. The results of electrical circuits simulation show the increase of the efficiency of the constructed first-order methods in comparison with methods of higher order.

MSC:

65Jxx Numerical analysis in abstract spaces
65-XX Numerical analysis
65Lxx Numerical methods for ordinary differential equations

Software:

LBNL
PDFBibTeX XMLCite
Full Text: DOI MNR

References:

[1] E.Hairer, G.Wanner, Solving ordinary differential equations, v. II, Stiff and differential-algebraic problems, Springer, Berlin, 1996 · Zbl 0859.65067
[2] E.A.Novikov, Explicit methods for stiff systems, Nauka, Novosibirsk, 1997 (in Russian) · Zbl 0934.65067
[3] E.A.Novikov, A.E.Novikov, “Explicit-Implicit Variable Structure Algorithm for Solving Stiff Systems”, International Journal of Mathematical Models and Methods in Applied Sciences, 9:1 (2015), 62-70
[4] E.A.Novikov, Yu.V.Shornikov, Computer simulation of stiff hybrid systems, Publisher of NSTU, Novosibirsk, 2012 (in Russian)
[5] A.E.Novikov, E.A.Novikov, “L-stable (2,1)-method for stiff nonautonomius problem solving”, Computing technologies, 13 (2008), 477-482 (in Russian)
[6] E.A.Novikov, Yu.A.Shitov, Integration algorithm for stiff systems based on a second-order accuracy (m, k)-method with numerical calculation of the Jacobi matrix, Preprint of the Exhibition Center of the Siberian Branch of the USSR Academy of Sciences № 20, Krasnoyarsk, 1988 (in Russian)
[7] E.A.Novikov, M.V.Rybkov, “The numerical algorithm of constructing stability polynomials of first order methods”, Bulletin of the Buryat State University, 2014, no. 9-2, 80-85 (in Russian)
[8] E.A.Novikov, M.V.Rybkov, “The numerical algorithm of constructing of stability regions for explicit methods”, Control systems and information technologies, 55:1.1 (2014), 173-177 (in Russian)
[9] Yozo Hida, Xiaoye S Li, David H Bailey, Quad-double arithmetic: algorithms, implementation, and application, Technical Report LBNL-46996, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, 2000
[10] L.V.Knaub, P.S.Litvinov, A.E.Novikov, M.V.Rybkov, “Solving Problems of Moderate Stiffness Using Methods of the First Order with Conformed Stability Domains”, University Scientific Journal, 22 (2016), 49-58
[11] R.H.Merson, “An operational methods for integration processes”, Proc. of Symp. on Data Processing, Weapons Research Establishment, Salisbury, Australia, 1957 · Zbl 0123.18209
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.