2008/10/28 by Nikesh S. Dattani, Dattani, Nikesh S.
Computer Science · Engineering · Mathematics · #33F05 #65-01 (Secondary) #65L20 (Primary) #Advanced Numerical Methods in Computational Mathematics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.0810.4965
openalex publication_date 2008/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A review of the most popular Linear Multistep (LM) Methods for solving Ordinary Differential Equations numerically is presented. These methods are first derived from first principles, and are discussed in terms of their order, consistency, and various types of stability. Particular varieties of stability that may not be familiar, are briefly defined first. The methods that are included are the Adams-Bashforth Methods, Adams-Moulton Methods, and Backwards Differentiation Formulas. Advantages and disadvantages of these methods are also described. Not much prior knowledge of numerical methods or ordinary differential equations is required, although knowledge of basic topics from calculus is assumed.