BibTex RIS Cite

Year 2017, Volume: 66 Issue: 2, 349 - 361, 01.08.2017

Ayşegül Kaplan Yılmaz Dereli

https://doi.org/10.1501/Commua1_0000000825
Cited By: 2

Abstract

References

  • D.H. Peregrine, Calculations of the development of an undular bore, J. Fluid Mech., 25(1966), 321-330.
  • T.B. Benjamin, J.L. Bona and J.J. Mahony, Model equations for waves in nonlinear dispersive systems, Phil. Trans. Roy. Soc. London A, 227(1972), 47-78.
  • L.R.T. Gardner, G.A. Gardner, F.A. Ayoub and N.K. Amein, Approximations of solitary waves of the MRLW equation by B-spline …nite elements, Arab. J. Sci. Eng., 22(1997), 183- 193.
  • P.J. Olver, Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Philos. Soc., 85(1979), 143-159.
  • A.K. Khalifa, K.R. Raslan and H.M. Alzubaidi, A …nite diğerence scheme for the MRLW and solitary wave interactions, Appl. Math. Comput., 189(2007), 346-354.
  • A.K. Khalifa, K.R. Raslan and H.M. Alzubaidi, Numerical study using ADM for the modi…ed regularized long wave equation, Appl. Math. Model., 32(2008), 2962-2972.
  • A.K. Khalifa, K.R. Raslan and H.M. Alzubaidi, A collocation method with cubic B-splines for solving the MRLW equation, J. Comput. Appl. Math., 212(2008), 406-418.
  • Y. Dereli, Numerical solutions of the MRLW Equation Using Meshless Kernel Based Method of Lines, International Journal of Nonlinear Science, 13(2012), 28-38.
  • Y. Dereli, Solitary wave solutions of the MRLW Equation Using Radial Basis Functions, Numerical Methods in Partial Diğerential Equations, 28(2012), 235-247.
  • K.R. Raslan and S.M. Hassan, Solitary Waves for the MRLW equation, Applied Mathematics Letters, 22(2009), 984-989.
  • S.B.G. Karakoç, Y. Uçar and N.M. Ya¼gmurlu, Numerical solutions of the MRLW equation by cubic B-spline Galerkin …nite element method, Kuwait J. Sci., 42(2015), 141-159.
  • P. Lancaster and K. Salkauskas, Surfaces generated by moving least square methods, Math- ematics of Computation, 87(1981), 141-158.
  • T. Roshan, A Petrov-Galerkin method for solving the generalized regularized long wave (GRLW) equation, Computers and Mathematics with Applications, 63(2012), 943-956.
  • ·I. Da¼g, D. Irk, and M. Sarı, The extended cubic B-spline algorithm for a modi…ed regularized long wave equation, Chin. Phys. B, 22(2013), 040207.
  • P. Keskin and D. Irk, Numerical solution of the MRLW equation using …nite diğerence method, International Journal of Nonlinear Science, 14(2012), 355-361.
  • W. Ju-Feng, B. Fu-Nong, and C. Yu-Min, A meshless method for the nonlinear generalized regularized long wave equation, Chinese Physics B, 20(2011), 030206.
  • F. Haq, S. Islam, and I.A. Tirmizi, A numerical technique for solution of the MRLW equation using quartic B-splines, Applied Mathematical Modelling, 34(2010), 4151-4160.
  • S.B.G. Karakoç, N.M. Ya¼gmurlu, and Y. Uçar, Numerical approximation to a solution of the modi…ed regularized long wave equation using quintic B-splines, Bundary Value Problems, 27(2013), 1-17.
  • B. ·Inan, A.R. Bahadır, Numerical Solutions of MRLW Equation by a Fully Implicit Finite- Diğerence Scheme, Journal of Mathematics and Computer Science, 15(2015), 228-239.
  • Current address : Ay¸se Gül Kaplan: Osmaniye Korkut Ata University, Mathematics Depart- ment, 80000, Osmaniye, Turkey
  • Current address : Yılmaz Dereli: Anadolu University, Mathematics Department, 26470, Es- ki¸sehir, Turkey

NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD

Year 2017, Volume: 66 Issue: 2, 349 - 361, 01.08.2017

Ayşegül Kaplan Yılmaz Dereli

https://doi.org/10.1501/Commua1_0000000825
Cited By: 2

Abstract

In this paper, the Modifed Regularized Long Wave (MRLW)equation is solved by using moving least square collocation (MLSC) method.To show the accuracy of the used method several numerical test examplesare given. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution is known L2, L1 error norms are calculated. Also mass, energy and momentum in variants are calculated for every test problem. Obtained numerical resultsare compared with some earlier works. According to the obtained results, the method is very efficient and reliable

Keywords

Moving least square collocation method MRLW equation

References

  • D.H. Peregrine, Calculations of the development of an undular bore, J. Fluid Mech., 25(1966), 321-330.
  • T.B. Benjamin, J.L. Bona and J.J. Mahony, Model equations for waves in nonlinear dispersive systems, Phil. Trans. Roy. Soc. London A, 227(1972), 47-78.
  • L.R.T. Gardner, G.A. Gardner, F.A. Ayoub and N.K. Amein, Approximations of solitary waves of the MRLW equation by B-spline …nite elements, Arab. J. Sci. Eng., 22(1997), 183- 193.
  • P.J. Olver, Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Philos. Soc., 85(1979), 143-159.
  • A.K. Khalifa, K.R. Raslan and H.M. Alzubaidi, A …nite diğerence scheme for the MRLW and solitary wave interactions, Appl. Math. Comput., 189(2007), 346-354.
  • A.K. Khalifa, K.R. Raslan and H.M. Alzubaidi, Numerical study using ADM for the modi…ed regularized long wave equation, Appl. Math. Model., 32(2008), 2962-2972.
  • A.K. Khalifa, K.R. Raslan and H.M. Alzubaidi, A collocation method with cubic B-splines for solving the MRLW equation, J. Comput. Appl. Math., 212(2008), 406-418.
  • Y. Dereli, Numerical solutions of the MRLW Equation Using Meshless Kernel Based Method of Lines, International Journal of Nonlinear Science, 13(2012), 28-38.
  • Y. Dereli, Solitary wave solutions of the MRLW Equation Using Radial Basis Functions, Numerical Methods in Partial Diğerential Equations, 28(2012), 235-247.
  • K.R. Raslan and S.M. Hassan, Solitary Waves for the MRLW equation, Applied Mathematics Letters, 22(2009), 984-989.
  • S.B.G. Karakoç, Y. Uçar and N.M. Ya¼gmurlu, Numerical solutions of the MRLW equation by cubic B-spline Galerkin …nite element method, Kuwait J. Sci., 42(2015), 141-159.
  • P. Lancaster and K. Salkauskas, Surfaces generated by moving least square methods, Math- ematics of Computation, 87(1981), 141-158.
  • T. Roshan, A Petrov-Galerkin method for solving the generalized regularized long wave (GRLW) equation, Computers and Mathematics with Applications, 63(2012), 943-956.
  • ·I. Da¼g, D. Irk, and M. Sarı, The extended cubic B-spline algorithm for a modi…ed regularized long wave equation, Chin. Phys. B, 22(2013), 040207.
  • P. Keskin and D. Irk, Numerical solution of the MRLW equation using …nite diğerence method, International Journal of Nonlinear Science, 14(2012), 355-361.
  • W. Ju-Feng, B. Fu-Nong, and C. Yu-Min, A meshless method for the nonlinear generalized regularized long wave equation, Chinese Physics B, 20(2011), 030206.
  • F. Haq, S. Islam, and I.A. Tirmizi, A numerical technique for solution of the MRLW equation using quartic B-splines, Applied Mathematical Modelling, 34(2010), 4151-4160.
  • S.B.G. Karakoç, N.M. Ya¼gmurlu, and Y. Uçar, Numerical approximation to a solution of the modi…ed regularized long wave equation using quintic B-splines, Bundary Value Problems, 27(2013), 1-17.
  • B. ·Inan, A.R. Bahadır, Numerical Solutions of MRLW Equation by a Fully Implicit Finite- Diğerence Scheme, Journal of Mathematics and Computer Science, 15(2015), 228-239.
  • Current address : Ay¸se Gül Kaplan: Osmaniye Korkut Ata University, Mathematics Depart- ment, 80000, Osmaniye, Turkey
  • Current address : Yılmaz Dereli: Anadolu University, Mathematics Department, 26470, Es- ki¸sehir, Turkey
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Ayşegül Kaplan This is me

Yılmaz Dereli This is me

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 2

Cite

APA Kaplan, A., & Dereli, Y. (2017). NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 349-361. https://doi.org/10.1501/Commua1_0000000825
AMA Kaplan A, Dereli Y. NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2017;66(2):349-361. doi:10.1501/Commua1_0000000825
Chicago Kaplan, Ayşegül, and Yılmaz Dereli. “NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 2 (August 2017): 349-61. https://doi.org/10.1501/Commua1_0000000825.
EndNote Kaplan A, Dereli Y (August 1, 2017) NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 349–361.
IEEE A. Kaplan and Y. Dereli, “NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 2, pp. 349–361, 2017, doi: 10.1501/Commua1_0000000825.
ISNAD Kaplan, Ayşegül - Dereli, Yılmaz. “NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (August 2017), 349-361. https://doi.org/10.1501/Commua1_0000000825.
JAMA Kaplan A, Dereli Y. NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:349–361.
MLA Kaplan, Ayşegül and Yılmaz Dereli. “NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 2, 2017, pp. 349-61, doi:10.1501/Commua1_0000000825.
Vancouver Kaplan A, Dereli Y. NUMERICAL SOLUTIONS OF THE MRLW EQUATION USING MOVING LEAST SQUARE COLLOCATION METHOD. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):349-61.

Cited By

Quintic Trigonometric B-spline Algorithm for Numerical Solution of the Modified Regularized Long Wave Equation
Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi
https://doi.org/10.53608/estudambilisim.1288254
Numerical solution of modified regularized long wave equation by using cubic trigonometric B-spline functions
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.25092/baunfbed.532578

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.