Application of Explicit Methods with Extended Stability Regions for Solving Stiff Problems
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https://elib.sfu-kras.ru/handle/2311/20245Author:
Novikov, Eugeny A.
Rybkov, Mikhail V.
Новиков, Е.А.
Рыбков, Михаил В.
Date:
2016-06Abstract:
An algorithm is developed to determine coefficients of the stability polynomials such that the explicit
Runge-Kutta methods have a predetermined shape and size of the stability region. Inequalities for accuracy
and stability control are obtained. The impact of the stability control on efficiency of explicit methods
to solving stiff problems is shown. Numerical calculations confirm that the three-step method of the first
order with extended stability region is more efficient than the traditional three-stage method of the third
order Разработан алгоритм определения коэффициентов полиномов устойчивости, при которых явные
методы типа Рунге-Кутта имеют заданные форму и размер области устойчивости. Получены
неравенства для контроля точности и устойчивости численных формул первого порядка. Ис-
следовано влияние контроля устойчивости на эффективность явных методов применительно к
решению жестких задач. Приведены результаты расчетов, показывающие повышение эффектив-
ности трехстадийного метода первого порядка с расширенной областью устойчивости в сравне-
нии с традиционным трехстадийным методом третьего порядка
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