Geodesic
First-order methods with extended stability regions for solving electric circuit problems
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 242-252

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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.
Keywords: stiff problem, explicit methods, stability region, accuracy and stability control. 
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     author = {Mikhail V. Rybkov and Lyudmila V. Knaub and Danil V. Khorov},
     title = {First-order methods with extended stability regions for solving electric circuit problems},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {242--252},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a10/}
}
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Mikhail V. Rybkov; Lyudmila V. Knaub; Danil V. Khorov. First-order methods with extended stability regions for solving electric circuit problems. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 242-252. http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a10/