Search results for "Homotopy analysis method"
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Discrete and differential homotopy in circular restricted three-body control
2010
The planar circular restricted three-body problem is considered. The control enters linearly in the equation of motion to model the thrust of the third body. The minimum time optimal control problem has two scalar parameters: The ratio of the primaries masses which embeds the two-body problem into the three-body one, and the upper bound on the control norm. Regular extremals of the maximum principle are computed by shooting thanks to continuations with respect to both parameters. Discrete and dierential homotopy are compared in connection with second order sucient conditions in optimal control. Homotopy with respect to control bound gives evidence of various topological structures of extr…
Solving a model for the evolution of smoking habit in Spain with homotopy analysis method
2013
We obtain an approximated analytical solution for a dynamic model for the prevalence of the smoking habit in a constant population but with equal and different from zero birth and death rates. This model has been successfully used to explain the evolution of the smoking habit in Spain. By means of the Homotopy Analysis Method, we obtain an analytic expression in powers of time t which reproduces the correct solution for a certain range of time. To enlarge the domain of convergence we have applied the so-called optimal convergence-control parameter technique and the homotopy-Padé technique. We present and discuss graphical results for our solutions. ©