奇異攝動延遲積分微分方程的Pouzet-Runge-Kutta方法.pdf

1、華中科技大學(xué)碩士學(xué)位論文奇異攝動延遲積分微分方程的Pouzet-Runge-Kutta方法姓名：趙飛申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：張誠堅20061025AbstractDelay differential equations(DDEs) often appear in auto-control, biology, physics,aerospace and economics.Singular perturbation de

2、lay problem(DSPPs) and delay dif-ferential algebraic problem are a special subproblem of delay differential equation.Fordiscrete type singularly perturbed delay problem, Gun SiQing had studied error behaviorabout Runge-K

3、utta methods and linear multi-step methods.Tian HongJiong had proved thesingularly perturbed delay problem was exponential stability,and gave out the expansionof true solution.Up to now,both abroad and home have no resul

4、ts about numerical solu-tion of singular perturbation delay problem.Moreover for singularly perturbed problem,because the solution near the origin is decay very fast, so studying the convergence ofnumerical solution is v

5、ery important.Therefor,In my paper we study the convergence ofPouzet-Runge-Kutta methods for singular perturbation delay integro-differential problem.At the fi rst chapter,we review the history of numerical solution for

6、delay differentialequation.At the second chapter,we discuss the ε-expansion of single variable and singlestiffness singular perturbation delay differential-integral problem.At the third chapter,westudy the multi-stiffnes

7、s singular perturbation delay differential-integral problem,and getthe global error of Pouzet-Runge-Kutta method for that problem.In the end,numericalexperiments can confi rm the results.At the forth chapter,we study the

8、 two variables andsingle stiffness singular perturbation delay differential-integral problem,and get the globalerror of Pouzet-Runge-Kutta method for that problem.Key words:Delay-integro-differential singularly perturbed