2020/12/29 by J. Nathan Kutz, Kutz, J. Nathan · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Numerical methods for differential equations #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.2012.14591
openalex publication_date 2020/12/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can help produce meaningful approximate solutions for many modern problems in the engineering and physical sciences. An overview of such methods is given here, focusing on the use of perturbation techniques for revealing many key properties and behaviors exhibited in practice across diverse scientific disciplines.