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Numerical solution of variational problems using exponential sextic spline

Arshad Khan|Pooja Khandelwal
장전수학회 (Jangjeon Mathematical Society)|2017.10|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제20권 제4호|pp. 545-562|DOI 10.17777/pjms.2017.20.4.003

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참고문헌

키워드

Boundary value problemCalculus of variationExponential sextic splineConvergence analysisTruncation error
주제분류수학

초록

In this paper, exponential sextic spline function is used for find- ing the numerical solution of boundary value problems which arise from the problems of calculus of variations. Spline relations are derived and direct methods of order two, four and six have been obtained. Convergence anal- ysis is brie y discussed. Numerical examples are given to demonstrate the eciency of the presented method. Comparisons are made to con rm the reliability and accuracy of the proposed technique.

Abstract

In this paper, exponential sextic spline function is used for find- ing the numerical solution of boundary value problems which arise from the problems of calculus of variations. Spline relations are derived and direct methods of order two, four and six have been obtained. Convergence anal- ysis is brie y discussed. Numerical examples are given to demonstrate the eciency of the presented method. Comparisons are made to con rm the reliability and accuracy of the proposed technique.

참고문헌 (20)

  1. J.H. Ahlberg, "The Theory of Splines and Their Appli-cations" (1967), Academic Press
  2. R.Y. Chang, "Shifted Legendre direct method for variational problems", J. Optim. Theory Appl., 39, pp.299~306 (1983)
  3. C.F. Chen, "A walsh series direct method for solving variational problems", J. Franklin Inst., 300, pp.265~280 (1975)
  4. M. Dehghan, "The use of Adomain decomposition method for solving prob-lems in calculus of variations", Math. Problem Engg, pp.1~12 (2006)
  5. S. Dixit, "Bernstein Direct Method for Solving Variational Problems", International Mathematical Forum, 5, pp.2351~2370 (2010)
  6. C. H. Hsiao, "Haar wavelet direct method for variational problems", Math. Comput. Sim-ulation, 64, pp.569~585 (2004)
  7. C. Hwang, "Laguerre series direct method for variational problems", J. Op-tim. Theory Appl, 39(1), pp.143~149 (1983)
  8. L. Elsgolts, "Differential Equations and the Calculus of Variations" (1973), Mir Publishers
  9. I. M. Gelfand, "Calculus of Variations" (1963), Prentice-Hall
  10. P.Henrici, "Discrete Variable Methods in Ordinary Differential Equations" (1962), John Wiley
  11. A. Khan, "Parametric cubic spline approach to the solution of a system of second-order boundary-value problems", J. Optim. Theory and Applics, 118, pp.45~54 (2003)
  12. A. Khan, "Parametric cubic spline solution of two point boundary value problems", Appl. Math. Comput., 154, pp.175~182 (2004)
  13. A. Khan, "Sextic spline solution of singularly perturbed boundary value problem", Appl. Math. Comput, 181, pp.432~439 (2006)
  14. A. Khan, "Non-polynomial sextic spline solution of singularly perturbed boundary-value problems", Int. J. Comput. Math, 19(5), pp.1122~1135 (2014)
  15. R. Mohammadi, "Numerical solution of calculus of variation problems via exponential spline method", Math. Sci. Lett, 4(2), pp.101~108 (2015)
  16. M. Razzaghi, "Legendre wavelets direct method for variational problems", Math. Comput. Simulation, 53, pp.185~192 (2000)
  17. A. Saadatmandi, "The numerical solution of problems in calculus of variation using chebyshev finite difference method", Phys. Lett. A, 372, pp.4037~4040 (2008)
  18. M. Zarebnia, "The numerical solution of problems in calculus of variation using B-spline collocation method", J. Appl. Math., pp.1~10 (2012)
  19. M. Zarebnia, "Numerical solution of the boundary value problems in calculus of variations using parametric cubic spline method", J. Inf. Comput. Sci, 8(4), pp.275~282 (2013)
  20. M. Zarebnia, "Numerical solution of variational problems via parametric quintic spline method", J. Hyperstruct, 3(1), pp.40~52 (2014)

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