A Numerical Methods And Stability Of Differential Algebraic Equations

Differential-algebraic equations(DAEs) are shown to play an important role in mathemati-cal models regarding a wide variety of scientific and engineering applications including multi-body mechanics, optimal control, electrical design, chemically reacting systems, biology andbiomedicine.In chapter2, the fundamental goal of this study has been to construct an approximation tonumerical solutions of linear constant coefficient DAE’s to study the problem of [8] and extendthe method to LTVDAEs.In chapter3, Drazin inverse is applied to solve the time varying differential algebraic equa-tions. This method is tested on a index-1Differential algebraic system. According to the obtainedsolutions we infer that Drazin inverse is a powerful tool for solving this kind of problems. FromTable,we know that the precision of the Drazin inverse method is higher than the Radau IIAmethod, but the Drazin inverse method is implemented more complex than the Radau IIA method.In chapter4, we study the stability of the time varying differential algebraic equations. we firstintroduce the concept of standard canonical form(SCF) of homogeneous systems and will hence-forth restrict the consideration to the case of systems which are transferable into SCF, then wederive some stability concepts of the homogeneous systems.