TITLE:
Consistency and Stability Issues in the Numerical Integration of the First and Second Order Initial Value Problem
AUTHORS:
Isaac Fried
KEYWORDS:
Initial Value Problems, Numerical Integration, Consistency, Stability, Multiple Solutions, Sensitivity to Initial Conditions, Slowing and Advancing the Computed Motion
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.8,
August
21,
2019
ABSTRACT: In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). Included are remarks on multiple solutions, multi-step methods, effect of initial value perturbations, as well as slowing and advancing the computed motion in second order problems.