A Survey in Mathematics for Industry Two-timing and matched asymptotic expansions for singular perturbation problems

作者：O'Malley R E Jr^*; Kirkinis E

来源：European Journal of Applied Mathematics, 2011, 22: 613-629.

DOI：10.1017/S0956792511000325

• Asymptotic methods
• Perturbation theory
• Boundary layers
• Multiple scales
• Amplitude equations

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations.

• 出版日期2011-12