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Bookkeeping parameter in perturbation methods. (English) Zbl 1072.34508
Summary: In case of no small parameter in an equation, we can expand the solution in a series of an artificial parameter. The artificial parameter is a bookkeeping or crutching device and is set equal to one after the “perturbation solution” is obtained. In order to avoid secular terms arising in a straightforward expansion, the coefficients in the equation are also expanded into series of the artificial parameter. Some examples are given, and the results show that the obtained approximate solutions are uniformly valid on the whole solution domain.

MSC:
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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[1] DOI: 10.1016/S1007-5704(99)90065-5 · Zbl 0932.34058
[2] He J.H., International Journal of Nonlinear Sciences and Numerical Simulation 1 (1) pp 51– (2000)
[3] DOI: 10.1006/jsvi.1999.2509 · Zbl 1235.70139
[4] DOI: 10.1016/S0020-7462(98)00085-7 · Zbl 1068.74618
[5] DOI: 10.1063/1.528326 · Zbl 0684.34008
[6] DOI: 10.1063/1.528998 · Zbl 0743.34021
[7] Andrianov I., International Journal of Nonlinear Sciences and Numerical Simulation 1 (4) pp 327– (2000) · Zbl 0977.35031
[8] DOI: 10.1016/S0020-7462(98)00048-1 · Zbl 1342.34005
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