Spline collocation approach to study Brachistochrone problem.

Resumen

In this paper authors discussed a problem of quickest descent, the Brachistochrone curve. Spline collocation method is used to solve the non-linear boundary value problem. The numerical results obtained are compared with the transformation method to show effectiveness and accuracy of this method.

Biografía del autor

Pinky M. Shah, Veer Narmad South Gujarat University.
Department of Mathematics.
Jyotindra C. Prajapati, Sardar Patel University.
Department of Mathematics.

Citas

Aravind P. K., Simplified Approach to Brachistochrone Problem, Amer. J. Phys., 49 (9), pp. 884-886, (1981).

Ashby N., Brittin W. E., Love W. F., Wyss W., Brachistochrone with Coulomb Friction, Amer. J. Phys., 43 (10), pp. 902-906, (1975).

Bickley W. G., Piecewise Cubic Interpolation and Two-Point Boundary Problems, The Computer Journal, 11, pp. 206-208, (1968).

Blue J. L., Spline Function Methods for Nonlinear Boundary Value Problems, Communications of the ACM, 12 (6), pp. 327-330, (1969).

Covic V., Veskovic M. Brachistochrone on a Surface with Coulomb Friction, Int. J. of Nonlinear Mechanics, 43, pp. 437-450, (2008).

Deboor C., Bicubic splines interpolation, J. Math. Phys., 41, pp. 212-218, (1962).

Denman H. H., Remarks on Brachistochrone Tautochrone Problem, Amer. J. Phys., 53 (3), pp. 224-227, (1985).

Dunham, William. Journey Through Genius, NewYork: Penguin Books, 1991.

Erlichson H.,Johann Bernoullis Brachistochrone Solution Using Fermats Principle of Least Time, Eur. J. Phys., 20, pp. 299-304, (1999).

Farina C., Bernoulli´s Method for Relativistic Brachistochrones, J. Phys. A: Math. Gen., 20, pp. L57-L59, (1987).

Gelfand and Fomin. I. M., S. V. Calculus of Variations. Englewood Cliffs, NJ: Prentice-Hall,Inc., 1963.

Goldstein. H. F., Bender. C. M., Relativistic Brachistochrone, J.Math.Phys.,27, pp. 507-511, (1986).

Hayen J. C.,Brachistochrone with Coulomb Friction, Int. J of NonLinear Mechanics 40, pp. 1057-1075, (2005).

Palmieri, Duzur The Brachistochrone Problem a New Twist to an Old Problem, Undergraduate Honors Thesis, Millers ville University of PA, (1996).

Parnovsky, A. S. Some Generalizations of the Brachistochrone Problem, Acta Physica Polonica, 93, (1998).

Scarpello G. M., Ritelli D., Relativistic Brachistochrone under Electric or Gravitational Uniform Field, Z. Angew. Math. Mech., 86, (9), pp. 736-743, (2006).

Sussmann and Willem: 300 Years of optimal control: From the Brachistochrone to the Maximum principle. Optimal-Control

Tee G., Isochrones and Brachistochrones, Neural,ParallelSci.Comput., 7, pp. 311-342, (1999).

Vander Heijden. A. M. A., Diepstraten J. D., On the Brachistochrone with Dry Friction, Int. J. Non-Linear Mech., 10, pp. 97-112, (1975).

Venezian G., Terrestrial Brachistochrone, Amer. J. Phys., 34 (8), 701, (1966).

Vratanar B., Saje M., On the analytical solution of the Brachistochrone Problem in a Neo conservative Field, Int. J. Non-Linear Mech., 33 (3), pp. 489-505, (1998).

Yamani H. A., Mulhem A. A., A Cylindrical Variation on the Brachistochrone Problem, Amer. J. Phys., 56 (5), pp. 467-469, (1988).

Publicado
2019-06-03
Cómo citar
[1]
P. Shah y J. Prajapati, «Spline collocation approach to study Brachistochrone problem»., Proyecciones (Antofagasta, En línea), vol. 38, n.º 2, pp. 353-362, jun. 2019.
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Artículos