**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32131

##### Non-Polynomial Spline Method for the Solution of Problems in Calculus of Variations

**Authors:**
M. Zarebnia,
M. Hoshyar,
M. Sedaghati

**Abstract:**

**Keywords:**
Calculus of variation; Non-polynomial spline functions; Numerical method

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1063202

**References:**

[1] R. Weinstock, Calculus of Variations: With Applications to Physics and Engineering, Dover, 1974.

[2] B. Horn, B. Schunck, Determining optical flow, Artificial Intelligence, vol. 17, no. (1-3), pp. 185-203, 1981.

[3] K. Ikeuchi, B. Horn, Numerical shape from shading and occluding boundaries. Artificial Intelligence,vol. 17,no. (1-3), pp. 141-184, 1981.

[4] L. Elsgolts, Differential Equations and Calculus of Variations, Mir, Moscow, 1977 (translated from the Russian by G. Yankovsky).

[5] I.M. Gelfand, S.V. Fomin, Calculus of Variations, Prentice-Hall, Englewood Cliffs, NJ, 1963.

[6] C.F. Chen, C.H. Hsiao, A walsh series direct method for solving variational problems, J. Franklin Inst.vol. 300, pp. 265-280, 1975.

[7] R.Y. Chang, M.L.Wang, Shifted Legendre direct method for variational problems, J. Optim. Theory Appl.vol. 39, pp. 299-306, 1983.

[8] I.R. Horng, J.H. Chou, Shifted Chebyshev direct method for solving variational problems, Internat. J. Systems Sci. vol. 16, pp. 855-861,1985.

[9] C. Hwang, Y.P. Shih, Laguerre series direct method for variational problems, J. Optim. Theory Appl. Vol. 39, no. 1, pp. 143-149, 1983.

[10] S. Dixit, V.K. Singh, A.K. Singh, O.P. Singh, Bernstein Direct Method for Solving Variational Problems, International Mathematical Forum,vol. 5, 2351-2370, 2010.

[11] M. Razzaghi, S. Yousefi, Legendre wavelets direct method for variational problems, Mathematics and Computers in Simulation, vol. 53, pp. 185-192, 2000.

[12] M. Tatari, M. Dehghan, Solution of problems in calculus of variations via He-s variational iteration method, Physics Letters A, vol. 362, pp. 401-406, 2007.

[13] J.H. Ahlberg, E.N. Nilson, J.L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York, 1967.

[14] T.N.E. Greville, Introduction to spline functions, in: Theory and Application of Spline Functions, Academic Press, New York, 1969.

[15] P.M. Prenter, Splines and Variational Methods, John Wiley & Sons INC., 1975

[16] G. Micula, Sanda Micula, Hand Book of Splines, Kluwer Academic Publisher-s, 1999.

[17] M.A. Ramadan, I.F. Lashien, W.K. Zahra, Polynomial and nonpolynomial spline approaches to the numerical solution of second order boundary value problems, Applied Mathematics and Computation ,vol. 184, pp. 476-484, 2007.

[18] A. Khan, Parametric cubic spline solution of two point boundary value problems, Applied Mathematics and Computation,vol. 154, pp. 175-182, 2004.