14 Perturbation Methods, Numerical Methods and Review
When an equation cannot be solved, two kinds of approximation remain. Perturbation methods exploit a small parameter to build analytic approximations that reveal how the solution depends on the parameters. Numerical methods compute a solution for given parameters to any desired accuracy. Each needs the other: perturbation theory tells the numerical analyst what to expect, and numerical solutions test the range of validity of perturbation formulas. This final section treats both, with the theory of the earlier sections (Gronwall’s inequality, Floquet theory, averaging) underpinning each method, and ends with a review of the course.
14.1 Regular perturbation and secular terms
14.2 The Poincaré–Lindstedt method
14.3 Averaging and multiple scales
14.4 Singular perturbation and boundary layers
14.5 Numerical methods
14.6 Review of the course
14.7 Perturbation and numerical methods in software
14.8 Practice Problems
14.2 The Poincaré–Lindstedt method
14.3 Averaging and multiple scales
14.4 Singular perturbation and boundary layers
14.5 Numerical methods
14.6 Review of the course
14.7 Perturbation and numerical methods in software
14.8 Practice Problems
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