Unlike traditional algorithms,the new algorithm is constructed by reducing the models to differential-algebraic equations with index 1 and using backward differentiation formulae with varable order and step size.

Asymptotic stability of θ-methods for differential-algebraic equations with several delays;

Dynamic equations of multi-body systems with holonomic constraints are differential-algebraic equations.

In numerically solving ordinary differential equations and differential-algebraic equations block methods are efficient.

Fundamental concepts in power system differential-algebraic equations (DAE) model, like singular point and multiple energy function sheets defined on constraint manifolds, are studied.

After the reduction of the degree of freedom and the proper transformation, the dynamic analysis of a braced frame with friction dampers sum up to solve a differential-algebraic equations of index 1.

Based on large deformation geometrical relations, a mathematical model described with differential algebraic equations is presented for axisymmetric hyperbolic thin-metal shells with variable thickness under internal pressure, which remedies the low precision in solving finite strain problems based on Gleyzal’s geometrical relations expanded with Taylor’s formula.

This paper is devoted to the application of the parallel multistep hybrid method to the numerical solution for a class of Index-2 differential algebraic equations,and the errors are estimated,it has obtained the extremely ideal result.

Simulation model described by the Modelica language can be translated into a system of differential algebraic equations.