We consider a special class of partitioned linearly-implicit Runge-Kutta methods for the solution of multibody systems in index 3 formulation. In contrast to implicit methods these methods require only the solution of linear systems for the algebraic variables. We study convergence and consistency of the methods and give numerical results for a special method of order 4 and comparisons.

Article history: Received 20 November 2012 Received in revised form 7 June 2013 Accepted 17 June 2013 Available online 1 July 2013

K e y w o r d s O r d i n a r y differential equations, Initial value problems, Runge-Kut ta methods, Stiffness detection, Symbolic computation, Computer algebra systems, Computer generation of numerical methods. 1. I N T R O D U C T I O N A framework for explicit Runge-Kutta methods is being implemented as part of an ongoing overhaul of MATHEMATICA~S differential equation solver NDSolve. One o...

We apply Patankar Runge–Kutta methods to y′ = M(y)y and focus on the case where M(y) is a graph Laplacian as resulting scheme will preserve positivity total mass. The second order Heun method tested using four test problems (stiff non-stiff) cast into this form. local error estimated step size chosen adaptively. Concerning accuracy efficiency, results are comparable those obtained with traditio...

The main di culty in the implementation of most standard implicit Runge-Kutta (IRK) methods applied to (sti ) ordinary di erential equations (ODE's) is to e ciently solve the nonlinear system of equations. In this article we propose the use of a preconditioner whose decomposition cost for a parallel implementation is equivalent to the cost for the implicit Euler method. The preconditioner is ba...

Enormous amount of real time robot arm research work is still being carried out in different aspects, especially on dynamics of robotic motion and their governing equations. Taha [5] discussed the dynamics of robot arm problems. Research in this field is still on-going and its applications are massive. This is due to its nature of extending accuracy in order to determine approximate solutions a...

In the context of solving nonlinear partial differential equations, Shu and Osher introduced representations of explicit Runge-Kutta methods, which lead to stepsize conditions under which the numerical process is totalvariation-diminishing (TVD). Much attention has been paid to these representations in the literature. In general, a Shu-Osher representation of a given Runge-Kutta method is not u...