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Cubic Spline Colocation Methods for Several Classes of Functional Diferential Equations

Author: SuHong
Tutor: WenLiPing
School: Xiangtan University
Course: Computational Mathematics
Keywords: ordinary differential equation delay differential equation differentialequations with variable delay neutral delay differential equation spline collocation method absolute stability A-stability P-stability
CLC: O241.81
Type: Master's thesis
Year: 2010
Downloads: 12
Quote: 1
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Abstract


In this paper, cubic spline collocation method for initial value of ordinarydifferential equationand initial value of delay differential equationare discussed. The main results are as follows:(1)Cubic spline collocation method for ordinary differential equations is constructedin this paper. The local truncation error, convergence and consistencyare also obtained. We have also discussed linear stability of this method andobtained nonlinear stability of this method which based on Lipschitz condition.(2)Cubic spline collocation method for delay differential equations is constructedin this paper. The local truncation error, convergence and consistencyare also obtained. We have also discussed linear stability of this method andobtained nonlinear stability of this method which based on Lipschitz condition.(3)Several numerical examples have been given in this paper, the results ofwhich successfully verified the theoretical results. Besides, we have applied cubicspline method to differential equations with variable delay and neutral delay differentialequations and got some satisfied results.

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