Fixed-point iteration for numerical solutions to equations in physics: Comment on “Solving introductory physics problems recursively using iterated maps” [Am. J. Phys., 93 , 336–343 (2025)]
Abstract
English et al. recently described a method for “Solving an introductory physics problem using an iterative map” [Am. J. Phys. 93, 336–343 (2025)]; however, because their map is only conditionally stable, its domain of validity is restricted to a subset of possible system parameters. Here, we address this limitation by presenting an alternative solution based on an iterative map that is unconditionally stable, and which therefore converges for any choice of system parameters. Our approach illustrates the importance of experimenting with a range of iteration schemes when using the fixed-point method to solve non-linear equations in physics.
Fields of Study & Subjects
Matrix Theory and Algorithms
Model Reduction and Neural Networks
Numerical methods for differential equations
Publication details
- Journal / source
- American Journal of Physics
- Publisher
- American Association of Physics Teachers (AAPT)
- Volume
- 94
- Issue
- 3
- Pages
- 253–254
- Publication date
- 19 February 2026
- Language
- EN