This paper extends the use of quantization–based integration methods to the simulation of hybrid systems. Using the fact that these methods approximate ordinary differential equations (ODEs) and differential algebraic equations (DAEs) by discrete event systems, it is shown how hybrid systems can be approximated by pure discrete event simulation models. In this way, the treatment and detection o...

In this paper, Numerical solution of Differential-Algebraic equations (DAEs) with index-3 is considered by Pade approximation. We applied this method to two examples. First differential-algebraic equations (DAEs) with index-3 has been converted to power series by one-dimensional differential transformation, Then the numerical solution of equation was put into Pade series form. Thus we obtained ...

Starting from the equations describing the equivalent dynamics of ordinary differential equations (ODEs), an equivalent dynamical differential algebraic equation (DAE) system is derived. It is shown that a procedure similar to the one available for ODEs can be used to construct an equivalent DAE system as well. The proposed method is shown to work with a class of discontinuous DAE systems typif...

The authors have developed a Taylor series method for solving numerically an initial-value problem differential algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit, see BIT 45:561–592, 2005 and BIT 41:364-394, 2001. Numerical results have shown this method to be efficient and very accurate, and particularly suitable for problems that are of too high an ...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...