Numerical Analysis Of One-Leg Methods For A Class Of Delay Differential Algebraic Equations

Delay differential algebraic equations arise widely in the fields of computer aided design,circuit analysis, mechanics system,mock chemical reaction and real-time emulation of auto-control system.So,researching this problem class has very important theoretical meaning and applied value .However,with delay item and restriction of algebraic condition,the analysis of this problem class is more difficult. there are a few articals which discuss the numerical methods of the equations.Stability of theoretical solution and numerical solution and D-convergence of numerical solution to delay differential algebraic equations are discussed in this paper.We obtain the following main results:1.We put forward a class of problem K_{α,β,γ}^(A) and discuss its stability and asymptotic stability.The sufficient conditions for stability and asymptotic stability of theoretical solution to the problem are obtained.2.We deduce the One-Leg method to solute this class of problem and discuss stability and asymptotic stability of this method. Furthermore, we extend GR-stability and GAR-stability in reference [11] to the class of delay differential algebraic equations K_{α,β,γ}^(A) and prove for One-Leg methods (p, a) that A-stability implies GR-stability and strong A-stability implies GAR-stability.3.We extend B-convergence in reference [61, 62] and D-convergence in reference [59] to the class of delay differential algebraic equations K_{α,β,γ}^(A) and put forward D_A-convergence. Furthermore,we discuss D_A-convergence of the problem and give its error estimate. Finally, it is proved that a One-Leg method with linear interpolation procedure is D_A -convergent of order p if it is A-stable and consistent of order p for ODEs, here p=1 or 2.4.In last chapter,we use several A-stable methods to test the above results. Numerical experiments show that the practice accord with the theory of this thesis.