first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

In this paper, the problem of dwell time for Hurwitz stability switched linear systems is considered. Dwell determined based on solution Lyapunov matrix equation differential systems. A numerical example illustrating efficiency theorem has been given.

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

The fractional calculus has many applications in applied science and engineering. The solution of the differential equation containing fractional derivative is much involved. An effective and easy-to-use method for solving such equations is needed. However not only the analytical solutions exist for a limited number of cases, but also the numerical methods are very complicated and difficult. In...

In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. for the efficient solution of the above mentioned problems, linear multistep methods or runge-kutta technique are used. for the simulation of chemical procedures the ra...

A new method to decide the invertibility of a given high-dimensional function over a domain is presented. The problem arises in the field of verified solution of differential algebraic equations (DAEs) related to the need to perform projections of certain constraint manifolds over large domains. The question of invertibility is reduced to a verified linear algebra problem involving first partia...