Singular Perturbation - Examples of Singular Perturbative Problems

Examples of Singular Perturbative Problems

Each of the examples described below shows how a naive perturbation analysis, which assumes that the problem is regular instead of singular, will fail. Some show how the problem may be solved by more sophisticated singular methods.

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Singular Perturbation - Examples of Singular Perturbative Problems - Algebraic Equations
... Consider the problem of finding all roots of the polynomial ... Singular perturbation analysis suggests that the cubic has another root ... In a sense, the problem has two different scales two of the roots converge to finite numbers as decreases, while the third becomes arbitrarily large ...

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