We discuss the use of the formal theory of differential equations in the numerical analysis of general systems of partial differential equations. This theory provides us with a very powerful and natural framework for generalising many ideas from differential algebraic equations to partial differential equations. We study in particular the existence and uniqueness of (formal) solutions, the meth...

A finite algorithm is developed for the solution of algebraic equations with integer exponents. It is established, by transformation to a matrix equation that a root of the algebraic equation can be determined in O(n) steps, where n is the degree. Mathematics Subject Classification: 12D10; 65H17

A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...

We discuss new discretization methods for linear differential–algebraic equations with variable coefficients. We introduce numerical methods to compute the local invariants of such differential–algebraic equations that were introduced by the authors in a previous paper. Using these quantitities we are able to determine numerically global invariances like the strangeness index, which generalizes...

A modification of the homotopy analysis method (HAM) for solving a system of nonlinear boundary value problems (BVPs) in semi–infinite domain, micropolar flow due to a linearly stretching of porous sheet, is proposed. This method is based on operational matrix of exponential Chebyshev functions to construct the derivative and product of the unknown function in the matrix form. In addition, by u...

Stabilization involves finding feedback controllers which stabilize the closed-loop system in the finite-time sense. Stability and control have been developed in the literature using Lyapunov-like method. In this paper, we develop a general framework for stabilization of linear differential-algebraic equations with time-varying delay. Based on Lyapunov-like function method and new bound estimat...

A shooting method for two{point{boundary value problems for fully implicit index{ 1 and {2 diierential{algebraic equations is presented. A combination of the shooting equations with a method of the calculation of consistent initial values leads to a system of nonlinear algebraic equations with nonsingular Jacobian. Examples are given.