The branching problem in generalized power solutions to differential equations

Details The branching problem in generalized power solutions to differential equations The branching problem in generalized power solutions to differential equations

2004-03-29

arxiv.org/abs/math/0403482v1

Mathematics and Computers in Simulation 67/1-2, 45-54 (2004)

Mathematics

Classical Analysis and ODEs

14 pages, elsart style, Mathematics and Computers in Simulation, Special Issue on Applications of Computer Algebra in Science,

Scientific paper

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.

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