The branching problem in generalized power solutions to differential equations. (English) Zbl 1058.65070
Summary: Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An algorithm to identify these critical values and generate the generalized power series for distinct families of solutions is presented, and as an application the singular behavior of a cosmological model with a nonlinear dissipative fluid is obtained. This algorithm has been implemented in the computer algebra system Maple.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 68W30 | Symbolic computation and algebraic computation |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 83F05 | Relativistic cosmology |
| 83-08 | Computational methods for problems pertaining to relativity and gravitational theory |
Keywords:
Generalized power series; Nonlinear ordinary differential equations; Symbolic computation; Cosmological models; numerical example; algorithmSoftware:
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