Qingyong Zhu

Sun Yat-Sen University, Shengcheng, Guangdong, China

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Publications (2)1.53 Total impact

  • Qi Wang, Qingyong Zhu
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    ABSTRACT: This paper deals with the stability analysis of the Runge-Kutta methods for a differential equation with piecewise continuous arguments of mixed type. The stability regions of the analytical solution are given. The necessary and sufficient conditions under which the numerical solution is asymptotically stable are discussed. The conditions under which the analytical stability region is contained in the numerical stability region are obtained and some numerical experiments are given.
    International Journal of Computer Mathematics 01/2011; 88:1052-1066. · 0.54 Impact Factor
  • Qi Wang, Qingyong Zhu, Mingzhu Liu
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    ABSTRACT: This paper is concerned with the numerical properties of θθ-methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two θθ-methods, namely the one-leg θθ-method and the linear θθ-method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained, and the conditions of oscillations for the θθ-methods are also obtained. It is proved that oscillations of the analytic solution are preserved by the θθ-methods. Furthermore, the relationships between stability and oscillations are revealed. Some numerical experiments are presented to illustrate our results.
    Journal of Computational and Applied Mathematics 01/2011; 235:1542-1552. · 0.99 Impact Factor