Published August 23, 2011 | Version 9998

Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations

Authors/Creators

Description

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.

Files

9998.pdf

Files (167.0 kB)

Name Size Download all
md5:f2d9ba7d23f0fbe84efcb29cf34ffad0
167.0 kB Preview Download

Additional details

References

  • L. Elsgolts, Differential Equations and Calculus of Variations, Mir, Moscow, 1977 (translated from the Russian by G. Yankovsky).
  • I.M. Gelfand, S.V. Fomin, Calculus of Variations, Prentice-Hall, Englewood Cliffs, NJ, 1963.
  • C.F. Chen, C.H. Hsiao, A walsh series direct method for solving variational problems, J. Franklin Inst.vol. 300, pp. 265-280, 1975.
  • R.Y. Chang, M.L.Wang, Shifted Legendre direct method for variational problems, J. Optim. Theory Appl.vol. 39, pp. 299-306, 1983.
  • I.R. Horng, J.H. Chou, Shifted Chebyshev direct method for solving variational problems, Internat. J. Systems Sci. vol. 16, pp. 855- 861,1985.
  • C. Hwang, Y.P. Shih, Laguerre series direct method for variational problems, J. Optim. Theory Appl. Vol. 39, no. 1, pp. 143-149, 1983.
  • 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.
  • M. Razzaghi, S. Yousefi, Legendre wavelets direct method for variational problems, Mathematics and Computers in Simulation, vol. 53, pp. 185-192, 2000.
  • 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.