The extended family of 2isd-methods for differential stiff systems
Автор: Vasilyev Evgeniy Ivanovich, Vasilyeva Tatyana Anatolyevna, Kiseleva Mariya Nikolaevna
Журнал: Математическая физика и компьютерное моделирование @mpcm-jvolsu
Рубрика: Прикладная математика
Статья в выпуске: 3 (28), 2015 года.
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The new set of absolutely stable difference schemes for a numerical solution of ODEs stiff systems (1) is submitted: d u(t) f (u), t 0, u(0) u0 dt . (1) The main feature of the set is the multi-implicit finite differences with the second derivatives of the desired solution. The expanded three-parameter (, , ) set of 2ISD-schemes (2)-(3) is studied in more details in this paper. 2 1 1 1 0 2 2 2 2 0 ( ф ) ф ( ф ) 2ф n n i i n i n i i n n i i n i n i i a E b J f a E b J f v v v v (2) 101 128 11 240 240 240 56 128 56 240 240 240 13 40 3 240 240 240 8 8 240 240 3б 2в 4в 3б 2в, 3г 3г б в 4б б в г 4г г ki ki a b (3) At arbitrary (, , ) parameters last difference equation in system (2) has 5th order of accuracy. We found that the set of absolutely stable 2ISD-schemes includes two families: the set of the L-stable schemes and the set of the schemes of heightened accuracy for linear problems. For example: at 1 б 168, в 0, г 0 we have A-stable scheme with 8th order of approximation, at 53 1 6 б 5880, в 148, г 315 we have L1-stable scheme with 7th order of approximation, at 23 1 14 б 360, в 60, г 315 we have L2-stable scheme with 6th order of approximation. The testing of this difference schemes on linear and nonlinear problems with a different stiff power is conducted. The errors of a numerical solution as functions of integration step size are computed in numerical experiments. These results demonstrate high quality of stability and accuracy of the suggested 2ISD-schemes.
L-устойчивость, l-stability, a-устойчивость, implicit methods, multi-implicit methods, methods with second derivative, а-stability, stiff systems
Короткий адрес: https://sciup.org/14968987
IDR: 14968987 | DOI: 10.15688/jvolsu1.2015.3.4