Application of pade approximants to numerical initial-value problems.

Two-point Pade approximants

We present analytic estimates for the energy levels of N electrons (N = 2−5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a smooth function of the parameter β=(effective Rydberg/effective dot energy)1/6. Two-point Pade approximants are obtained from the series expansions of the energy ...

Stiffness in numerical initial-value problems

This paper reviews various aspects of stiffness in the numerical solution of initial-value problems for systems of ordinary differential equations. In the literature on numerical methods for solving initial value problems the term "stiff" has been used by various authors with quite different meanings, which often causes confusion. This paper attempts to clear up this confusion by reviewing some...

Numerical Methods for Fuzzy Initial Value Problems

In this paper, fuzzy initial value problems for modelling aspects of uncertainty in dynam­ ical systems are introduced and interpreted from a probabilistic point ofview. Due to the uncertainty incorporated in the model, the behavior of dynamical systems modelIed in this way will generally not be unique. Rather, we obtain a large set of trajectories which are more or less compatible with the des...

Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems

In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...

Numerical solution of fuzzy initial value problems under generalized dierentiability by HPM