A User’s View of Solving Stiff Ordinary Differential Equations

Lawrence F. Shampine (1) , Charles William Gear (2)

1 SNL - Sandia National Laboratories [Albuquerque]
2 Department of Computer Science

This paper aims to assist the person who needs to solve stiff ordinary differential equations. First we identify the problem area and the basic difficulty by responding to some fundamental questions: Why is it worthwhile to distinguish a special class of problems termed "stiff"? What are stiff problems? Where do they arise? How can we recognize them? Second we describe the characteristics shared by methods for the numerical solution of stiff problems. These characteristics have important implications as to the convenience and efficiency of solution of even routine problems. Understanding them is indispensable to [he assembling of codes for the very efficient solution of special problems or for solving exceptionally large problems at all. Third we shall briefly discuss what is meant by "solving" a differential equation numerically and what might be reasonably expected in the case of stiff problems.

Domaines: Equations aux dérivées partielles [math.AP]; Mathématiques [math]

Lawrence F. Shampine, Charles William Gear. A User’s View of Solving Stiff Ordinary Differential Equations. SIAM Review, 1979, 21 (1), pp.1 - 17. ⟨10.1137/1021001⟩. ⟨hal-01711390⟩