| A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence |
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| 作者姓名： | Leng Xin Liu Degui Song Xiaoqiu & Chen Lirong. Beijing Inst. of Computer Application and Simulation Technology Beijing P. R. China . Beijing Inst. of Applied Physics and Computational Mathematics Beijing P. R. China |
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| 作者单位： | Leng Xin 1，2，Liu Degui 1，2，Song Xiaoqiu1 & Chen Lirong11. Beijing Inst. of Computer Application and Simulation Technology，Beijing 100854，P. R. China;2. Beijing Inst. of Applied Physics and Computational Mathematics，Beijing 100088，P. R. China |
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| 摘 要： | 1.INTRODUCTION Considerthefollowingdelaydifferentialequations(DDEs)y′(x)=f(x,y(x),y(x-τ(x))),a≤x≤b y(x)=φ(x),xmin≤x≤a(1)wherey,f,φaren vectorfunctions,φ(x)isinitial valuefunction,τ(x)≥0isdelayfunction.Definition1DDEs(1)issingularatthepoint xαifthelagsatisfiesτ(xα)=0.Ifthereisnosuch pointxα∈a,b],thentheDDEs(1)isnon singular.InthenumericalsolutionofDDEs(1)byacon tinuousexplicitRunge Kuttamethod,wesuppose thatwehaveanapproximationyntoy(x)atxnand wishtocomputeanapproxima…
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A class of two-step continuity Runge-Kutta methods for solving singular delay differential equations and its convergence |
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| Leng Xin ,,Liu Degui ,,Song Xiaoqiu & Chen Lirong. Beijing Inst. of Computer Application and Simulation Technology,Beijing ,P. R. China,. Beijing Inst. of Applied Physics and Computational Mathematics,Beijing ,P. R. China.A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence[J].Journal of Systems Engineering and Electronics,2005,16(4). |
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| Authors: | Leng Xin Liu Degui Song Xiaoqiu Chen Lirong |
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| Institution: | 1. Beijing Inst. of Computer Application and Simulation Technology, Beijing 100854, P. R. China;Beijing Inst. of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
2. Beijing Inst. of Computer Application and Simulation Technology, Beijing 100854, P. R. China |
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| Abstract: | An idea of relaxing the effect of delay when computing the RungeKutta stages in the current step and a class of twostep continuity RungeKutta methods (TSCRK) is presented. Their construction, their order conditions and their convergence are studied. The twostep continuity RungeKutta methods possess good numerical stability properties and higher stageorder, and keep the explicit process of computing the RungeKutta stages. The numerical experiments show that the TSCRK methods are efficient. |
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| Keywords: | convergence singular delay differential equations twostep continuity RungeKutta methods |
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