본문 바로가기
KERD
논문KCI 등재

New analytic approximate solutions to the generalized regularized long wave equations

Necdet Bildik|Sinan Deniz
대한수학회 (The Korean Mathematical Society)|2018.05|대한수학회보 (Bulletin of the KMS)|제55권 제3호|pp. 749-762

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

partial differential equationssolitonsoptimal perturbation iteration methodregularized long wave equations
주제분류수학

초록

In this paper, the new optimal perturbation iteration method has been applied to solve the generalized regularized long wave equation. Comparing the new analytic approximate solutions with the known exact solutions reveals that the proposed technique is extremely accurate and effective in solving nonlinear wave equations. We also show that,unlike many other methods in literature, this method converges rapidly to exact solutions at lower order of approximations.

Abstract

In this paper, the new optimal perturbation iteration method has been applied to solve the generalized regularized long wave equation. Comparing the new analytic approximate solutions with the known exact solutions reveals that the proposed technique is extremely accurate and effective in solving nonlinear wave equations. We also show that,unlike many other methods in literature, this method converges rapidly to exact solutions at lower order of approximations.

참고문헌 (36)

  1. Y. Aksoy, "New perturbation-iteration solutions for Bratu-type equations", Computers & Math. Appl., 59(8), pp.2802~2808 (2010)[DOI]
  2. Y. Aksoy, "New perturbation-iteration solutions for nonlinear heat transfer equations", Int. J. Numer. Methods for Heat & Fluid Flow, 22(7), pp.814~828 (2012)[DOI]
  3. Md. N. Alam, "Application of the Novel (G", G)-expansion method to the regularized long wave equation, 2015, pp.1, 20~37
  4. H. M. Baskonus, "Analytical solutions for nonlinear long-short wave interaction systems with highly complex", J. Comput. Appl. Math., 312, pp.257~266 (2017)[DOI]
  5. A. Bekir, "New solitons and periodic wave solutions for some nonlinear physical models by using the sine-cosine method", Phys. Scripta, 77(4), pp.045008~ (2008)[DOI]
  6. D. Bhardwaj, "A computational method for regularized long wave equation", Computers & Math. Appl., 40(12), pp.1397~1404 (2000)[DOI]
  7. N. Bildik, "Comparative study between optimal homotopy asymptotic method and perturbation-iteration technique for different types of nonlinear equations", Iranian J. Sci. Techno. Transactions A: Science, pp.1~8
  8. N. Bildik, "A new efficient method for solving delay differential equations and a comparison with other methods", European Physical Journal Plus, 132(1), pp.51~ (2017)[DOI]
  9. J. L. Bona, "Stable and unstable solitary-wave solutions of the generalized regularized long-wave equation", J. Nonlinear Sci., 10(6), pp.603~638 (2000)[DOI]
  10. J. L. Bona, "A comparison of solutions of two model equations for long waves, in Fluid dynamics in astrophysics and geophysics (Chicago, Ill., 1981), Lectures in Appl. Math., 20", pp.235~267 (1983), Amer. Math. Soc.
  11. I. Dag, "Approximation of the RLW equation by the least square cubic B-spline finite element method", Appl. Math. Model., 25, pp.221~231 (2001)[DOI]
  12. M. Dehghan, "The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas", Comput. Phys. Comm., 182(12), pp.2540~2549 (2011)[DOI]
  13. S. Deniz, "A new analytical technique for solving Lane-Emden type equa-tions arising in astrophysics", Bull. Belg. Math. Soc. Simon Stevin, 24(2), pp.305~320 (2017)
  14. A. Dogan, "Numerical solution of regularized long wave equation using Petrov-Galerkin method", Comm. Numer. Methods Engrg., 17(7), pp.485~494 (2001)[DOI]
  15. A. Dogan, "Numerical solution of RLW equation using linear finite elements within Galerkins method", Appl. Math. Model., 26, pp.771~783 (2002)[DOI]
  16. R. S. Dubey, "Homotopy Perturbation Approximate Solutions for Bergman-Minimal Blood Glucose-Insulin Model", J. Fractal Geom. Nonlinear Anal. in Medicine and Biology (FGNAMB), 2(3), pp.1~6 (2016)
  17. L. R. T. Gardner, "A B-spline finite element method for the regularized long wave equation", Comm. Numer. Methods Engrg., 11(1), pp.59~68 (1995)[DOI]
  18. S. Iqbala, "Some solutions of the linear and nonlinear Klein-Gordon equations using the optimal homotopy asymptotic method", Appl. Math. Comput., 216(10), pp.2898~2909 (2010)
  19. H. Jafari, "Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition", Appl. Math. Comput., 180(2), pp.488~497 (2006)
  20. P. C. Jain, "Numerical solutions of the regularized long-wave equation", Comput. Methods Appl. Mech. Engrg., 20(2), pp.195~201 (1979)[DOI]
  21. D. Kaya, "A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation", Appl. Math. Comput., 149(3), pp.833~841 (2004)
  22. M. A. Khan, "Solitary wave solutions for the boussinesq and fisher equations by the modified simple equation method", Math. Lett., 2(1), pp.1~18 (2016)
  23. J. Lin, "High-order compact difference scheme for the regularized long wave equation", Comm. Numer. Methods Engrg, 23(2), pp.135~156 (2007)
  24. V. Marinca, "Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer", International Communications in Heat and Mass Transfer, 35(6), pp.710~715 (2008)[DOI]
  25. D. Mirzaei, "MLPG method for transient heat conduction problem with MLS as trial approximation in both time and space domains", CMES Comput. Model. Eng. Sci., 72(3), pp.185~210 (2011)
  26. M. Mohammadi, "Solving the generalized regularized long wave equation on the basis of a reproducing kernel space", J. Comput. Appl. Math., 235(14), pp.4003~4014 (2011)[DOI]
  27. T. Ozis, "He's homotopy perturbation method for solving heat-like and wave-like equations with variable coefficients", Phys. Lett. A, 372(38), pp.5944~5950 (2008)[DOI]
  28. D. H. Peregrine, "Calculations of the development of an undular bore", J. Fluid Mech., 25, pp.321~330 (1996)
  29. M. M. Rashidi, "Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method", Communications in Nonlinear Science and Numerical Simulation, 14(3), pp.708~717 (2009)[DOI]
  30. B. Saka, "A collocation method for the numerical solution of the RLW equation using cubic B-spline basis", Arab. J. Sci. Eng. Sect. A Sci., 30(1), pp.39~50 (2005)
  31. B. Saka, "A numerical solution of the RLW equation by Galerkin method using quartic B-splines", Comm. Numer. Methods Engrg., 24(11), pp.1339~1361 (2008)
  32. A. Shokri, "A meshless method using the radial basis functions for numerical solution of the regularized long wave equation", Numer. Methods Partial Differential Equations, 26(4), pp.807~825 (2010)
  33. D. Sinan, "Optimal Perturbation Iteration Method for Solving Nonlinear Heat Transfer Equations", J. Heat Transfer, 139(7), pp.074503~ (2017)[DOI]
  34. D. Sinan, "Applications of optimal perturbation iteration method for solving nonlinear differential equations", AIP Conference Proceedings, 1798(1) (2017)
  35. A. A. Soliman, "Numerical simulation of the generalized regularized long wave equation by He's variational iteration method", Math. Comput. Simulation, 70(2), pp.119~124 (2005)[DOI]
  36. K. A. Touchent, "Nonlinear fractional partial differential equations systems solutions through a hybrid homotopy perturbation Sumudu transform method", Nonlinear Studies, 22(4), pp.591~600 (2015)

관련 논문AI추천

The multisoliton solution of generalized Burger's equation by the formal linearization methodMohammad Mirzazadeh, Nasir Taghizadeh대한수학회 · 대한수학회논문집2011 · 제26권 제2호Kink wave solutions to KdV-Burgers equation with forcing termMukhiddin Muminov, Yusuf Buba Chukkol대한수학회 · 대한수학회논문집2020 · 제35권 제2호Application of Bifurcation Method to a Generalized Modified Boussinesq EquationChengxi Yang, Ming Song경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제1호COMPARISON DIFFERENTIAL TRANSFORM METHOD WITH ADOMIAN DECOMPOSITION METHOD FOR NONLINEAR INITIAL VALUE PROBLEMSEDA YULUKLU장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제1호Solutions of a class of singular second-order IVPs by variational homotopy perturbation methodM. Mahdavi, M. Matinfar장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제4호A New Combined Homotopy-Laplace Decomposition Method for Solving DDEs of Order (1, 2)Ananth Kumar S. R., R. Rangarajan장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제1호

이 간행물의 다른 논문 (23건)

On asymptotic of extremes from generalized Maxwell distributionJianjun Wang, Jianwen Huangpp. 679-698A note on proof of Gordon's ConjectureKun Dupp. 699-715Complete weight enumerators of some classes of linear codes with a few weightsZihui Liu, Yiwei Liupp. 717-734Asymptotic behavior of solutions for the generalized MHD and Hall-MHD systems in $\mathbb{R}^n$Mingxuan Zhupp. 735-747Operations on elliptic divisibility sequencesOsman Bizim, Betul Gezerpp. 763-776
원문 보기