Abstract
This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs). At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs.
Highlights
The general differential algebraic equations (DAEs)F (t, x (t), x (t)) = 0 (1)arise in many applications, circuit analysis, control theory, chemical process simulations, singular perturbation, constrained mechanical systems of rigid bodies, and so forth [1,2,3]
This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs)
We propose a finite algorithm to compute the Drazin inverse of the time varying DAEs
Summary
Arise in many applications, circuit analysis, control theory, chemical process simulations, singular perturbation, constrained mechanical systems of rigid bodies, and so forth [1,2,3]. In [4,5,6], the numerical solutions of constant coefficient DAEs were studied by Golub et al The linear time varying of DAE. In [11], Song had treated general higher index time varying linear DAEs in terms of matrix pencils and investigated their basic properties and their solvability. These results, the numerical solutions of DAEs seldom are involved. We shall consider the constant coefficient and time varying DAEs with different numerical methods.
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