| A-stable Explicit Nonlinear Runge-Kutta Methods |
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| 作者姓名： | 曹阳 李庆扬 |
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| 作者单位： | Cao Yang，Li Qingyang Department of Applied Mathematics，Tsinghua University，Beijing 100084 |
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| 基金项目： | Supported by the National Natural Science Foundationof China(No.195 710 4 6 ) |
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| 摘 要： | IntroductionConsidertheinitialvalueproblem(IVP):y′=f(x,y),y(x0)=y0(1)wherey∈RN,f:R×RN→RN.ThispaperisparticularlyinterestedinIVPsarisingfromchemicalreactionsandautomaticcontrolsystems1-4],whichareusuallystiff.ThesolutionofstiffIVPshasattractedinterest…
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A-stable Explicit Nonlinear Runge-Kutta Methods |
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| Cao Yang,Li Qingyang.A-stable Explicit Nonlinear Runge-Kutta Methods[J].Tsinghua Science and Technology,1998(4). |
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| Authors: | Cao Yang Li Qingyang |
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| Institution: | Cao Yang,Li Qingyang Department of Applied Mathematics,Tsinghua University,Beijing 100084 |
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| Abstract: | Nonlinear methods are combined with Runge Kutta methods to develop A stable explicit nonlinear Runge Kutta methods for solving stiff differential equations and a class of the third order formulae are constructed.It avoids solving the nonlinear equations which implicit methods must solve. Implementation is very simple and the computation cost for each step is small.This paper uses a shift transformation to avoid the order reduction of nonlinear methods at y = 0 . Thus the method is very practicable. Numerical tests show that the method is more efficient than explicit methods or implicit methods of the same order. |
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| Keywords: | stiff equations A stability nonlinear methods Runge Kutta methods nonlinear Runge Kutta methods |
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