Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems
We present a new numerical method for the computation of the forcing term of minimal norm such that a two-point boundary value problem admits a solution. The method relies on the following steps. The forcing term is written as a (truncated) Chebyshev series, whose coefficients are free parameters. A...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/895876 |
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| author | Gianni Arioli |
| author_facet | Gianni Arioli |
| author_sort | Gianni Arioli |
| collection | DOAJ |
| description | We present a new numerical method for the computation of the forcing term of minimal norm such that a two-point boundary value problem admits a solution. The method relies on the following steps. The forcing term is written as a (truncated) Chebyshev series, whose coefficients are free parameters. A technique derived from automatic differentiation is used to solve the initial value problem, so that the final value is obtained as a series of polynomials whose coefficients depend explicitly on (the coefficients of) the forcing term. Then the minimization problem becomes purely algebraic and can be solved
by standard methods of constrained optimization, for example, with Lagrange multipliers. We provide an application of this algorithm to the planar restricted three body problem in order to study the planning of low-thrust transfer orbits. |
| format | Article |
| id | doaj-art-12f4678299de464b88f8a5228ef9462f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-12f4678299de464b88f8a5228ef9462f2025-02-03T01:21:25ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/895876895876Optimization of the Forcing Term for the Solution of Two-Point Boundary Value ProblemsGianni Arioli0Dipartimento di Matematica “F. Brioschi”, Modellistica e Calcolo Scientifico (MOX), Politecnico di Milano, Via Bonardi 9, 20133 Milano, ItalyWe present a new numerical method for the computation of the forcing term of minimal norm such that a two-point boundary value problem admits a solution. The method relies on the following steps. The forcing term is written as a (truncated) Chebyshev series, whose coefficients are free parameters. A technique derived from automatic differentiation is used to solve the initial value problem, so that the final value is obtained as a series of polynomials whose coefficients depend explicitly on (the coefficients of) the forcing term. Then the minimization problem becomes purely algebraic and can be solved by standard methods of constrained optimization, for example, with Lagrange multipliers. We provide an application of this algorithm to the planar restricted three body problem in order to study the planning of low-thrust transfer orbits.http://dx.doi.org/10.1155/2013/895876 |
| spellingShingle | Gianni Arioli Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems Journal of Mathematics |
| title | Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems |
| title_full | Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems |
| title_fullStr | Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems |
| title_full_unstemmed | Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems |
| title_short | Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems |
| title_sort | optimization of the forcing term for the solution of two point boundary value problems |
| url | http://dx.doi.org/10.1155/2013/895876 |
| work_keys_str_mv | AT gianniarioli optimizationoftheforcingtermforthesolutionoftwopointboundaryvalueproblems |