{"title":"Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations","authors":"M. Zarebnia, N. Aliniya","volume":56,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1402,"pagesEnd":1408,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9998","abstract":"In this paper, a numerical solution based on sinc\r\nfunctions is used for finding the solution of boundary value problems\r\nwhich arise from the problems of calculus of variations. This\r\napproximation reduce the problems to an explicit system of algebraic\r\nequations. Some numerical examples are also given to illustrate the\r\naccuracy and applicability of the presented method.","references":"[1] L. Elsgolts, Differential Equations and Calculus of Variations, Mir,\r\nMoscow, 1977 (translated from the Russian by G. Yankovsky).\r\n[2] I.M. Gelfand, S.V. Fomin, Calculus of Variations, Prentice-Hall,\r\nEnglewood Cliffs, NJ, 1963.\r\n[3] C.F. Chen, C.H. Hsiao, A walsh series direct method for solving\r\nvariational problems, J. Franklin Inst.vol. 300, pp. 265-280, 1975.\r\n[4] R.Y. Chang, M.L.Wang, Shifted Legendre direct method for variational\r\nproblems, J. Optim. Theory Appl.vol. 39, pp. 299-306, 1983.\r\n[5] I.R. Horng, J.H. Chou, Shifted Chebyshev direct method for solving\r\nvariational problems, Internat. J. Systems Sci. vol. 16, pp. 855-\r\n861,1985.\r\n[6] C. Hwang, Y.P. Shih, Laguerre series direct method for variational\r\nproblems, J. Optim. Theory Appl. Vol. 39, no. 1, pp. 143-149, 1983.\r\n[7] S. Dixit, V.K. Singh, A.K. Singh, O.P. Singh, Bernstei Direct Method\r\nfor Solving Variational Problems, International Mathematical\r\nForum,vol. 5, 2351-2370, 2010.\r\n[8] M. Razzaghi, S. Yousefi, Legendre wavelets direct method for\r\nvariational problems, Mathematics and Computers in Simulation, vol.\r\n53, pp. 185-192, 2000.\r\n[9] A. Saadatmandi, M. Dehghan, The numerical solution of problems in\r\ncalculus of variation using Chebyshev finite difference method, Physics\r\nLetters A, vol. 372, pp. 4037- 4040, 2008.\r\n[10] F. Stenger, Numerical Methods Based on Sinc and Analytic Functions,\r\nSpringer-Verlag, New York, 1993. [11] J. Lund, K. Bowers, Sinc\r\nMethods for Quadrature and Differential Equations, SIAM,\r\nPhiladelphia, PA , 1992.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 56, 2011"}