A numerical algorithm for solving stiff boundary value problems with turning points is presented. The stiff systems are characterized as singularly perturbed differential equations. The numerical method is derived by appropriately discretizing the boundary layer and connection theory for such systems. Numerical results demonstrate the effectiveness of the method. In many cases the calculation p...

In this paper we analyze the consistency and stability properties of Runge-Kutta discrete adjoints. Discrete adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. The consistency analysis uses the concept of elementary differentials and reveals that the discrete Runge-Kutta adjoint method has the same order o...

Oscillatory integrals are present in many applications, and their numerical approximation is the subject of this paper. Contrary to popular belief, their computation can be achieved efficiently, and in fact, the more oscillatory the integral, the more accurate the approximation. We review several existing methods, including the asymptotic expansion, Filon method, Levin collocation method and nu...

Two point fully implicit block method of variable step size is developed for solving directly the second order system of Ordinary Differential Equations (ODEs). This method will estimate the solutions of Initial Value Problems (IVPs) at two points simultaneously. The method developed is suitable for the numerical integration of non stiff and mildly stiff differential systems. Numerical results ...

In this paper, we introduce a method to solve linear stiff IVPs. The suggested method, which we call modified homotopy perturbation method, can be considered as an extension of the homotopy perturbation method (HPM) which is very efficient in solving a varety of differential and algebraic equations. In this work, a class of linear stiff initial value problems (IVPs) are solved by the classical ...

OBJECTIVE To examine the prevalence of medical conditions and use of health services among young adults with Down syndrome and describe the impact of these conditions upon their lives. METHODS Using questionnaire data collected in 2011 from parents of young adults with Down syndrome we investigated the medical conditions experienced by their children in the previous 12 months. Univariate, lin...

Block Runge-Kutta formulae suitable for the approximate numerical integration of initial value problems for first order systems of ordinary differential equations are derived. Considered in detail are the problems of varying both order and stepsize automatically. This leads to a class of variable order block explicit Runge-Kutta formulae for the integration of nonstiff problems and a class of v...