Title   name
KSIAM 2006 Annual Meeting
  Speaker   Lee, Chang-Ock  
  Date 2006-11-25
  Place 건국대학교
  File  의 1 번째 Real Media 동영상입니다. 의 1 번째 강연자료입니다.
Abstract : Many phenomena of interest in physiology and biochemistry are characterized by reactionsamong several chemical species and diffusion in various mediums (see [4–7]). In a closed system,both reactions and diffusion are governed by a system of ordinary differential equations(ODEs)˙ y(t) = My(t), (1)which guarantees conservation of the total amount of y(t) for any t  0. Since we are concernedwith the steady-state solution as well as the transient in simulations of very large systemsof chemical reactions or molecular dynamics, we need to take the overall computationalcost into consideration. Many physiologists and biochemists prefer explicit methods to implicitmethods since implementation of the explicit methods is easier than the others. The popularmethods for reaction systems are simple explicit schemes such as Euler’s method, Runge-Kuttamethod, etc. However, it is well-known that conditional stability, the typical weak point ofexplicit methods, is very fatal for stiff problems. In the past few decades, many studies on numericalmethods for stiff ODEs have been done in various aspects (see [1–3]).The aim of this talk is to present two absolutely stable explicit schemes which are applicable toa general reaction system (1). The proposed methods are motivated by the simple exact solverfor a reversible reaction. In spite of their explicitness, we have unconditional stability, that is,stability without any condition on the step size. Furthermore, we proved the convergence of theproposed methods; one is of first order and the other is of second order.