Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32127
Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations

Authors: M. Zarebnia, N. Aliniya


In this paper, a numerical solution based on sinc functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Sinc functions; Galerkin; Numerical method

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1829


[1] L. Elsgolts, Differential Equations and Calculus of Variations, Mir, Moscow, 1977 (translated from the Russian by G. Yankovsky).
[2] I.M. Gelfand, S.V. Fomin, Calculus of Variations, Prentice-Hall, Englewood Cliffs, NJ, 1963.
[3] C.F. Chen, C.H. Hsiao, A walsh series direct method for solving variational problems, J. Franklin Inst.vol. 300, pp. 265-280, 1975.
[4] R.Y. Chang, M.L.Wang, Shifted Legendre direct method for variational problems, J. Optim. Theory Appl.vol. 39, pp. 299-306, 1983.
[5] I.R. Horng, J.H. Chou, Shifted Chebyshev direct method for solving variational problems, Internat. J. Systems Sci. vol. 16, pp. 855- 861,1985.
[6] C. Hwang, Y.P. Shih, Laguerre series direct method for variational problems, J. Optim. Theory Appl. Vol. 39, no. 1, pp. 143-149, 1983.
[7] S. Dixit, V.K. Singh, A.K. Singh, O.P. Singh, Bernstei Direct Method for Solving Variational Problems, International Mathematical Forum,vol. 5, 2351-2370, 2010.
[8] M. Razzaghi, S. Yousefi, Legendre wavelets direct method for variational problems, Mathematics and Computers in Simulation, vol. 53, pp. 185-192, 2000.
[9] A. Saadatmandi, M. Dehghan, The numerical solution of problems in calculus of variation using Chebyshev finite difference method, Physics Letters A, vol. 372, pp. 4037- 4040, 2008.
[10] F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer-Verlag, New York, 1993.
[11] J. Lund, K. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, PA , 1992.