Recently Ch. Lubich proved convergence results for Runge-Kutta methods applied to stii mechanical systems. The present paper discusses the new ideas necessary to extend these results to general linear methods, in particular BDF and multistep Runge-Kutta methods. Stii mechanical systems arise in the modelling of mechanical systems containing strong springs and (or) elastic joints. A typical exam...

ÐHighly-accurate solutions for the lid-driven cavity ̄ow are computed by a Chebyshev collocation method. Accuracy of the solution is achieved by using a substraction method of the leading terms of the asymptotic expansion of the solution of the Navier±Stokes equations in the vicinity of the corners, where the velocity is discontinuous. Critical comparison with former numerical experiments con®r...

Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. ...

A linear multistep method for solving first order initial value problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to first order initial value problems of ordinary differential equations. This implementation strategy is more accurat...

We describe a new method for numerical integration, dubbed bandlimited collocation implicit Runge–Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in Astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. This new method allows us to use significantly fewer force function evaluations than explicit ...

A B-spline finite element method is used to solve the equal width equation numerically. This approach involves a collocation method using quintic B-splines at the knot points as element shape. Time integration of the resulting system of ordinary differential equations is effected using the fourth order Runge–Kutta method, instead of the finite difference method, the resulting system of ordinary...