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Alternative Methods of Regular and Singular Perturbation Problems
Department of Engineering, United Tribes Technical College, Bismarck, North Dakota, USA
Department of Engineering, United Tribes Technical College, Bismarck, North Dakota, USA
Department of Environmental Science, United Tribes Technical College, Bismarck, North Dakota, USA
- 1 Department of Engineering, United Tribes Technical College, Bismarck, North Dakota, USA
- 2 Department of Engineering, United Tribes Technical College, Bismarck, North Dakota, USA
- 3 Department of Environmental Science, United Tribes Technical College, Bismarck, North Dakota, USA
Applied Mathematics·Volume 15 (2024)·Pages 687–708·Published 11 October 2024·DOI10.4236/am.2024.1510040
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Abstract
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.
KeywordsPerturbationRegular PerturbationSingular PerturbationAsymptotic ExpansionMatched AsymptoticStrained CoordinatesMultiple Scales
- Nayfeh, A.H. (2000) Perturbation Methods. Wiley. https://doi.org/10.1002/9783527617609
- Dalla Riva, M., Lanza de Cristoforis, M. and Musolino, P. (2021) Singularly Perturbed Boundary Value Problems. A Functional Analytic Approach, Springer.
- Walter, A. (2007) Mathematics for Physics and Physicists. Princeton University Press.
- Nayfeh, A.H. (2011) Introduction to Perturbation Techniques. Wiley.
- Kevorkian, J. and Cole, J.D. (1981) Introduction. In: Kevorkian, J. and Cole, J.D., Eds., Perturbation Methods in Applied Mathematics, Springer, 1-16. https://doi.org/10.1007/978-1-4757-4213-8_1
- Hinch, E.J. (1991) Perturbation Methods. Cambridge University Press. https://doi.org/10.1017/cbo9781139172189
- Holmes, M. (1995) Introduction to Perturbation Methods. Springer.
- Kevorkian, J. and Cole, J.D. (1996) Multiple Scale and Singular Perturbation Methods. Springer.
- Simmonds, J.G. and Mann, Jr. (1997) A First Look at Perturbation Theory. Dover Publications.
- O’Malley, R.E. (1991) Singular Perturbation Methods for Ordinary Differential Equations. Springer.
- Hunter, J.K. (2004) Asymptotic Analysis and Singular Perturbation Theory. University of California at Davis.