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...

We have begun to appreciate that the extent of this disorder is much wider than merely mental retardation. It is also a common cause of learning and emotional problems in mildly affected female carriers with normal IQs. These children present an enormous challenge to all child-care providers, be they in medicine, education, or in various therapy disciplines. Early identification is essential, a...

Social behaviors among two genetically homogeneous groups--girls with fragile X (fraX) or Turner syndrome (TS)--were examined to address the role of family environment versus biological determinants of social dysfunction in girls with these disorders. Using a sibling pair design, girls with fraX or TS were compared with their own sisters on measures of IQ and social functioning. The 8 girls wit...

We consider an integro-differential stiff problem, which can be used as a model for the vibrations of a body with hnear viscoelasticity at large times First, the problem is introduced in the framework of the theory of semigroups in Hubert spaces and then, an asymptotic expansion ofihe solution is obtained Fwally, it is shown the double convergence, when e —• 0 + , ofthe eigenvalues of the probl...

A multistep method with matricial coefficients is developed. It can be used to solve stiff initial value problems of the form y’= Ay + g(x,y). This method bears the nature of the classical Adams-Bashforth-Moulton PC formula and can be shown to be consistent, convergent and A-stable. A careful reformulation of this method legitimatizes the implementation of this algorithm in a variable-step vari...

In the recently developed Krylov deferred correction (KDC) methods for ordinary differential equation initial value problems [11], a Picard-type collocation formulation is preconditioned using low-order time integration schemes based on spectral deferred correction (SDC), and the resulting system is solved efficiently using a Newton-Krylov method. Existing analyses show that these KDC methods a...

Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value Problems (IVPs) is proposed. MATLAB versions for autonomous and non-autonomous ODEs of this algorithm have been implemented. These implementations have been compared with othe...

This paper proposes a new bilateral control scheme to ensure both transparency and robust stability under unknown constant time delay in stiff environment. Furthermore, this method guaranties suitable performance and robust stability when transition occurs between soft and stiff environments. This framework is composed of an adaptive sliding mode controller and an adaptive impedance controller,...