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

The strict-contractivity and the convergence of General Linear Methods on the classes of strictly dissipative and dissipative differential systems regarding some inner product are analyzed. New convergence and contractivity results of the methods on semi-infinite intervals are provided for the case of strictly dissipative problems. Some applications of the main results to the class of Runge-Kut...

In this paper, a hybrid technique of differential quadrature method and Runge-Kutta fourth order method is employed to analyze reaction-diffusion problems. The obtained results are compared with the available analytical ones. Further, a parametric study is introduced to investigate the influence of reaction and diffusion characteristics on behavior of the obtained results. Index Term-Reaction-d...

To calculate the trajectory of a rocket by use of a digital computer, the equations of the motion of the rocket should be solved step-by-step with respect to short intervals of time. Hence, the problem is essentially to solve the differential equations and thus there is no particular difficulty in the procedure. In a previous paper, the fundamental programming for the Runge-Kutta integration me...

Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...

This paper gives a modification of a class of stochastic Runge-Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

In this paper a domain Ω ⊆ C is a connected open set. We let O Ω denote the algebra of holomorphic functions on Ω. We will use the following notation: D denotes the unit disc in the complex plane. We let D2 D × D denote the bidisc, and D D × D × · · · × D the polydisc in C. The symbol B Bn is the unit ball in C. A domainΩ ⊆ C is said to be Runge if any holomorphic f onΩ is the limit, uniformly ...

_________________________________________________ Vernon W. Ruttan is Regents Professor in the Department of Applied Economics and in the Department of Economics at the University of Minnesota. This paper draws on two earlier papers (Ruttan, 1998; in press). I am indebted to Donald N. Duvick, Nicholas Kalaitzandonakes, John M. Reilly, C. Ford Runge, W. Burt Sundquist, and Paul E. Waggoner for c...