Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59063", author = "M. Zarebnia and N. Aliniya", title = "Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations", abstract = "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", volume = "5", number = "8", pages = "1339-6", }