Perturbation Methods and Computer Algebra in Mechanics
Perturbation methods are a collection of diverse schemes for obtaining approximate analytic solutions to problems which involve a small parameter ϵ, usually in the form of a power series in ϵ In these notes we will discuss computer algebra treatments of regular perturbations (section 2), and of three singular perturbation methods (composite expansions, section 4, averaging, section 5 and two variable expansion method, section 8).
KeywordsHopf Bifurcation Perturbation Method Computer Algebra Transition Curve Jacobian Elliptic Function
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- 9.R.H. Rand, “The Use of Symbolic Computation in Perturbation Analysis”, in Symbolic Computation in Fluid Mechanics and Heat Transfer, ed. H.H. Bau et al., ASME publication HTD-105/AMD-97, pp.41–45 (1988)Google Scholar
- 10.R.H. Rand, “Using Computer Algebra to Handle Elliptic Functions in the Method of Averaging”, in Symbolic Computations and Their Impact on Mechanics, eds. A.K. Noor, I. Elishakoff, G. Hulbert, pp.311–326, Amer.Soc.Mech.Eng., PVP-Vol.205, (1990)Google Scholar