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Global Stability of Differential Equations with Piecewise Continuous Arguments and the Convergence of Exponential Runge-Kutta

Author: LY Mohamed（LiMu）
Tutor: LiuMingZhu
School: Harbin Institute of Technology
Course: Computational Mathematics
Keywords: Delay differential equations Independent variable piecewise continuous differential equations Global Stability Order of convergence Index Runge-Kutta methods Exponential Euler method
CLC: O241.8
Type: Master's thesis
Year: 2010
Downloads: 18
Quote: 0
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Abstract


This article discusses a wide range of independent variables used to describe the population model with piecewise continuous differential equations (EPCA) analytical and numerical solutions for global stability . Global stability analysis has important theoretical value and practical significance . The first section reviews some of the basic concepts, including : stability , vibration , global stability , periodic solutions and boundedness . The second section discusses the global stability of the EPCA more independent variables with constant coefficients and variable coefficients . Global stability conditions are essentially improved . Exponential Runge-Kutta method is applied to solve the corresponding ordinary differential equation in this type of model , and discuss the index shows that Euler order of convergence of the the index implicit Euler method and index midpoint formula . Finally, exponential Runge-Kutta methods applied to the EPCA model and proved Index Euler method , the the index implicit Euler method and the index of midpoint formula to maintain its original order of convergence . Some experiments illustrate these methods is to maintain the global asymptotic stability of the model .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
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