| 1. |
- Anderson, Dan, 1943, et al.
(författare)
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Approximate solution of a Thomas-Fermi model equation for bulk self-gravitating stellar objects in two dimensions
- 2017
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Ingår i: European journal of physics. - : Institute of Physics (IOP). - 0143-0807 .- 1361-6404. ; 38, s. 1-8
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Tidskriftsartikel (refereegranskat)abstract
- Direct variational methods are used to find simple approximate solutions of the Thomas–Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the non-relativistic and ultra-relativistic cases. The approximate solutions are compared and shown to be in good agreement with exact and numerically obtained solutions.
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| 2. |
- Anderson, Dan, 1943, et al.
(författare)
-
Galerkin approach to approximate solutions of some nonlinear oscillator equations
- 2010
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Ingår i: American Journal of Physics. - : American Association of Physics Teachers (AAPT). - 0002-9505 .- 1943-2909. ; 78:9, s. 920-924
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Tidskriftsartikel (refereegranskat)abstract
- An analysis based on the Galerkin method is given of some nonlinear oscillator equations that have been analyzed by several other methods, including harmonic balance and direct variational methods. The present analysis is shown to provide simple yet accurate approximate solutions of these nonlinear equations and illustrates the usefulness and the power of the Galerkin method. (C) 2010 American Association of Physics Teachers. [DOI: 10.1119/1.3429974]
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| 3. |
- Anderson, Dan, 1943, et al.
(författare)
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Introduction to direct variational and moment methods and an application to the Child-Langmuir law
- 2015
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Ingår i: European Journal of Physics. - : IOP Publishing. - 1361-6404 .- 0143-0807. ; 2015:36, s. 065032-
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Tidskriftsartikel (refereegranskat)abstract
- A short introduction is given of direct variational methods and its relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions of difficult physical equations. A pedagogicalapplication of moment methods is given to the physically and technically important Child–Langmuir law in electron physics. The analysis is shown to provide simple, yet accurate, approximate solutions of the two-dimensionalproblem (a problem which does not allow an exact analytical solution)and illustrates the usefulness and the power of moment methods.
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| 4. |
- Anderson, Dan, 1943, et al.
(författare)
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The least uncomfortable journey from A to B
- 2016
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Ingår i: American Journal of Physics. - : American Association of Physics Teachers (AAPT). - 0002-9505 .- 1943-2909. ; 84:9, s. 690-695
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Tidskriftsartikel (refereegranskat)abstract
- A short introduction is given about direct variational methods and their relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions to difficult physicalequations. An application of these methods is given in the form of the variational problem of minimizing the discomfort experienced during different journeys, between two fixed horizontal points while keeping the travel time constant. The analysis is shown to provide simple, yet accurate, approximate solutions of the problem and illustrates the usefulness and the power of direct variational and moment methods. It also demonstrates the problem of a priori assessing the accuracy of the approximate solutions and illustrates that the variational solution does not necessarily provide a more accurate solution than that obtained by moment methods.
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| 5. |
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| 6. |
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| 7. |
- Rosenberg, C.-J., et al.
(författare)
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Diffusion of super-Gaussian profiles
- 2007
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Ingår i: European journal of physics. - : Institute of Physics Publishing, Bristol, BS1 6BE, United Kingdom. - 0143-0807 .- 1361-6404. ; 28, s. 45-50
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Tidskriftsartikel (refereegranskat)
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| 8. |
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