1979/01/01 by L. F. Shampine, C. W. Gear · 331 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Artificial intelligence #Backward differentiation formula #Calculus (dental) #Class (philosophy) #Collocation method #Computer science #Differential equation #Electromagnetic Simulation and Numerical Methods #Exact differential equation #Explicit and implicit methods #L-stability #Mathematical analysis #Mathematics #Numerical methods for differential equations #Ordinary differential equation #Stiff equation
paper · open access · doi:10.1137/1021001
published in SIAM Review 21(1), 1-17 (Society for Industrial and Applied Mathematics)
openalex publication_date 1979/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/19
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 the 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.