Perturbation Methods in the Computer Age |
Contents
1 | 1 |
Asymptotic Expansion of Integrals | 17 |
SingularPerturbation Methods | 77 |
Copyright | |
7 other sections not shown
Common terms and phrases
Airy function assume asymptotic expansion asymptotic methods asymptotic sequence behavior boundary conditions boundary layer branch cut branch point C₁ Cauchy's Integral Theorem coefficients complex conclude constant contour integration damped defined determine the leading-order differential equations Duffing's equation evaluate exact solution example Figure find the leading-order first-order problem Fourier integral Gamma function Hence inner and outer inner expansion integrand Jordan's Lemma Laplace integral Laplace's Method leading-order term Mach number matching Method of Stationary Method of Steepest multiple-scale analysis numerical O(eČ oscillator outer expansion perturbation methods perturbation solution real axis regular-perturbation problem Riemann surfaces Riemann-Lebesgue Lemma saddle point scale secular terms sin(t sinČ singular singular-perturbation sint small parameter Stationary Phase Steepest Descent subsection Substituting into Equation Taylor series theory turbulence variable velocity Watson's Lemma wherefore yields zeroth zeroth-order problem αξ მი მყ