The purpose of this work is to introduce a new idea how avoid the factorization large matrices during solution stiff systems ODEs. Starting from general form an explicit linear multistep method we suggest adaptively choose its coefficients on each integration step in order minimize norm residual implicit BDF formula. Thereby reduce number unknowns n O(1), where dimension ODE system. We call typ...

Abstract In the context of coupling hyperbolic problems, maximum stable time step an explicit numerical scheme may depend on design procedure. If this is case, procedure sensitive to changes in model parameters independent Courant–Friedrichs–Levy condition. This sensitivity can cause artificial stiffness that degrades performance a scheme. To overcome problem, we present systematic and general ...

The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary differential equation system by applying a generalized Schur complement. Applying the explicit Euler time integration scheme to this system results in a small maximum s...

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of LaneEmden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-...

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...

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...