Nonlinear equations in Physics, and their resolution using high order multi-step iterative methods
This work provides the physics teacher with theoretical and computational foundations to solve nonlinear equations, very com-mon in solving physical problems. In the present research three physics problems are solved, which are: a sphere floating in water, non-free fall of a parachutist, compression...
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| Formato: | Artículo revista |
| Lenguaje: | Español Portugués |
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Asociación de Profesores de Física de la Argentina
2021
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| Acceso en línea: | https://revistas.unc.edu.ar/index.php/revistaEF/article/view/36000 |
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| Sumario: | This work provides the physics teacher with theoretical and computational foundations to solve nonlinear equations, very com-mon in solving physical problems. In the present research three physics problems are solved, which are: a sphere floating in water, non-free fall of a parachutist, compression of a real spring; making use of principles related to fluids, kinematics and dynamics. Nonlinear equations are obtained which are difficult and, in some cases, impossible to be solved by means of analyti-cal methods. To find an approximate solution to these equations we use iterative methods starting from traditional methods such as Newton, Secant, Steffensen to the introduction of multi-step methods with high order of convergence such as Traub, Ostrowski and methods of order eight designed from Ostrowski's method. Finally, an analysis of the results obtained by applying all these methods to each of the selected physical problems is carried out and, in this way, establish which iterative method is more appropriate in each situation. |
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