Author(s)

Boampong Asare^1*, Manohar Sah¹, Ram Krishna Hona²

¹Department of Engineering, United Tribes Technical College, Bismarck, North Dakota, USA.
²Department of Environmental Science, United Tribes Technical College, Bismarck, North Dakota, USA.

Making exact approximations to solve equations distinguishes applied mathematicians from pure mathematicians, physicists, and engineers. Perturbation problems, both regular and singular, are pervasive in diverse fields of applied mathematics and engineering. This research paper provides a comprehensive overview of algebraic methods for solving perturbation problems, featuring a comparative analysis of their strengths and limitations. Serving as a valuable resource for researchers and practitioners, it offers insights and guidance for tackling perturbation problems in various disciplines, facilitating the advancement of applied mathematics and engineering.

Perturbation, Regular Perturbation, Singular Perturbation, Asymptotic Expansion, Matched Asymptotic, Strained Coordinates, Multiple Scales

Asare, B. , Sah, M. and Hona, R. (2024) Alternative Methods of Regular and Singular Perturbation Problems. Applied Mathematics, 15, 687-708. doi: 10.4236/am.2024.1510040.