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A septic B-spline finite element method for solving the nonlinear Schrödinger equation

Bülent SAKA|Idris Dag
장전수학회 (Jangjeon Mathematical Society)|2016.07|Advanced Studies in Contemporary Mathematics|제26권 제3호|pp. 527-540

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참고문헌

키워드

CollocationSchrödinger EquationSolitonSeptic B-spline
주제분류수학

초록

The septic B-spline collocation algorithm is set up to …nd the numerical solution of the nonlinear Schrödinger equation. The e¤ect of use of the higher degree B-spline in the collocation method is searched for getting the numerical solution of the Schrödinger equation. The three test problems are studied to show the robustness of the suggested method.

Abstract

The septic B-spline collocation algorithm is set up to …nd the numerical solution of the nonlinear Schrödinger equation. The e¤ect of use of the higher degree B-spline in the collocation method is searched for getting the numerical solution of the Schrödinger equation. The three test problems are studied to show the robustness of the suggested method.

참고문헌 (27)

  1. V. I. Karpman, "Modulated waves in nonlinear dispersive media", Soviet Phys. JETP, 28, pp.277~281 (1969)
  2. V. E. Zakharov, "Exact theory of two-dimensional self-focusing and one-dimensional self modulation of waves in nonlinear media", Soviet Phys. JETP, 34, pp.62~69 (1972)
  3. A. C. Scott, "The soliton: A new concept in applied science", Proc. IEEE, 61, pp.1443~1483 (1973)
  4. P. M. Prenter, "Splines and variational methods" (1975), J. Wiley
  5. T. R. Taha, "Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, Nonlinear Schrödinger Equation", J. Comput. Phys, 55, pp.203~230 (1984)
  6. J. Argyris, "An engineer’s guide to soliton phenomena: Appli-cation of the …nite element method", Comput. Meth. Appl. Mech. Engrg, 61, pp.71~122 (1987)
  7. Y. Tourigny, "An investigation into the e¤ect of product ap-proximation in the numerical solution of the cubic nonlinear Schrödinger equa-tion", J. Comput. Phys, 76, pp.103~130 (1988)
  8. L. R. T. Gardner, "A Leapfrog algorithm and stability studies for the nonlinear Schrödinger equation", Arab. J. Sci. Eng, 18, pp.23~32 (1993)
  9. L. R. T. Gardner, "B-spline …nite element studies of the nonlinear Schrödinger equation", Comput. Meth. Appl. Mech. Engrg, 108, pp.303~318 (1993)
  10. M. P. Robinson, "Note: On the numerical solution of the cubic Schrödinger equation in one space variable", J. Comput. Phys, 104, pp.277~284 (1993)
  11. M. P. Robinson, "Orthogonal spline collocation methods for Schrödinger-type equations in one space variable", Numer. Math, 68, pp.355~376 (1994)
  12. M. P. Robinson, "The solution of nonlinear Schrödinger equations using orthog-onal spline collocation", Comput. Math. Appl, 33, pp.39~57 (1997)
  13. I. Dag, "A quadratic B-spline …nite element method for solving nonlinear Schrödinger equation", Comput. Meth. Appl. Mech. Engrg, 174, pp.247~258 (1999)
  14. Q. Sheng, "Solving the generalized nonlinear Schrödinger equation via quartic spline approximation", J. Comput. Phys, 166, pp.400~417 (2001)
  15. G. Fairweather, "Trends in Industrial and Applied Mathematics", pp.219~250 (2002), Kluwer Academic Publishers
  16. S. A. Khuri, "A complex tanh-function method applied to nonlinear equations of Schrödinger type", Chaos, Solitons and Fractals, 20, pp.1037~1040 (2004)
  17. A Krowiak, "Symbolic computing in spline-based di¤erential quadrature method", Commun. Numer. Meth. Engng, 22, pp.1097~1107 (2006)
  18. S. M. El-Sayed, "A numerical solution and an exact explicit solution of the NLS equation", Appl. Math. Comput, 172, pp.1315~1322 (2006)
  19. B. Saka, "Quartic B-spline collocation method to the numerical so-lutions of the Burgers’equation", Chaos, Solitons and Fractals, 32, pp.1125~1137 (2007)
  20. A. M. Wazwaz, "A study on linear and nonlinear Schrödinger equations by the variational iteration method", Chaos, Solitons and Fractals, 37, pp.1136~1142 (2008)
  21. A. Korkmaz, "A di¤erential quadrature algorithm for nonlinear Schrödinger equation", Nonlinear Dyn, 56, pp.69~83 (2009)
  22. Y. Dereli, "Soliton solutions for NLS equation using radial basis functions", Chaos, Solitons and Fractals, 42, pp.1227~1233 (2009)
  23. B. Saka, "A Quintic B-spline Finite Element Method for Solving the Nonlinear Schrödinger Equation", Physics of Wave Phenomena, 20, pp.107~117 (2012)
  24. M. Aksoy, "Taylor Collocation Method for the Numerical Solution of the Nonlinear Schrödinger Equation Using Quintic B-Spline Basis", Physics of Wave Phenomena, 20, pp.67~79 (2012)
  25. Y. Dereli, "The meshless kernel-based method of lines for the numerical solution of the nonlinear Schrödinger equation", Engng. Anal. Boun. Elem, 36, pp.1416~1423 (2012)
  26. M. Aksoy, "Taylor-Collocation Method for The Numerical Solution of The Nonlinear Schrödinger Equation Using Cubic B-Spline Basis", Inter. J. of Nonlinear Sci, 15, pp.322~333 (2013)
  27. B. Saka, "A Quartic B-spline Collocation Method for Solving the Nonlinear Schrödinger Equation", Appl. Comput. Math, 14, pp.75~86 (2015)

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