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A New Algorithm Based on the Decic (tenth degree) B-spline Functions for Numerical Solution of the Equal Width Equation

Year 2022, , 185 - 194, 30.12.2022
https://doi.org/10.30931/jetas.1072151

Abstract

In this study, a new algorithm is introduced for the numerical solution of equal width (EW) equation. This algorithm is created by using the collocation finite element method based on decic B-spline functions for the space discretization of the EW equation and the Crank-Nicolson method for the time discretization of his equation. The obtained results are compared with the previous ones to see the efficiency and accuracy of the proposed method.

References

  • [1] Morrison, P.J., Meiss, J.D., Carey, J.R., "Scattering of RLW solitary waves", Physica 11D (1984) : 324-336.
  • [2] Gardner, L.R.T., Gardner, G.A., "Solitary waves of the equal width wave equation", Journal of Computational Physics 101 (1992) : 218-223.
  • [3] Irk, D., "B-Spline Galerkin solutions for the equal width equation", Physics of Wave Phenomena 20(2) (2012) : 122-130.
  • [4] Dağ, İ., Saka, B., Irk, D., "Galerkin method for the numerical solution of the RLW equation using quintic B-splines", Journal of Computational and Applied Mathematics 190 (2006) : 532-547.
  • [5] Saka, B., "A finite element method for equal width equation", Applied Mathematics and Computation 175 (2006) : 730-747.
  • [6] Saka, B., Dag, I., Dereli, Y., Korkmaz, A., "Three different methods for numerical solution of the EW equation", Engineering analysis with boundary elements 32 (2008) : 556-566.
  • [7] Dag, I., Irk, D., Boz, A., "Simulation of EW wave generation via quadratic B-spline finite element method", International Journal of Mathematics and Statistics 1 (A07) (2007) : 46-59.
  • [8] Esen, A., "A numerical solution of the equal width wave equation by a lumped Galerkin method", Applied Mathematics and Computation 168 (2005) : 270-282.
  • [9] Raslan, K.R., "Collocation method using quartic B-spline for the equal width (EW) equation", Applied Mathematics and Computation 168(2) (2005) : 795-805.
  • [10] Dağ, İ., Saka, B., "A cubic B-spline collocation method for the EW equation", Mathematical and Computational Applications 90 (2004) : 381-392.
  • [11] Dag, I., Ersoy, O., "The exponential cubic B-spline algorithm for equal width equation", Advanced Studies in Contemporary Mathematics 25(4) (2015) : 525-535.
  • [12] Yağmurlu, N.M., Karakaş, A.S., "Numerical solutions of the equal width equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization", Numerical Methods for Partial Differential Equations 36(5) (2020) : 1170-1183.
  • [13] Irk, D., Saka, B., Dağ, İ., "Cubic spline collocation method for the equal width equation", Hadronic Journal Supplement 18 (2003) : 201-214.
  • [14] Saka, B., Irk, D., Dağ, İ., "A numerical study of the equal width equation", Hadronic Journal Supplement 18 (2003) : 99-116.
  • [15] Banaja, M.A., Bakodah, H.O., "Runge-Kutta integration of the equal width wave equation using the method of lines", Mathematical Problems in Engineering 2015 (2015) : Article ID 274579.
  • [16] Inan, B., Bahadır, A.R., "A numerical solution of the equal width wave equation using a fully implicit finite difference method", Turkish Journal of Mathematics and Computer Science 2(1) (2014) : 1-14.
  • [17] Zaki, S.I., "A least-squares finite element scheme for the EW equation", Communications in Numerical Methods in Engineering 189 (2000) : 587-594.
  • [18] Doğan, A., "Application of Galerkin's method to equal width wave equation", Applied Mathematics and Computation 160 (2005) : 65-76.
  • [19] Roshan, T., "A Petrov-Galerkin method for equal width equation", Applied Mathematics and Computation 218(6) (2011) : 2730-2739.
  • [20] Gardner, L.R.T., Gardner, G.A., Ayoub, F.A., Amein, N.K., "Simulations of the EW undular bore", Communications in Numerical Methods in Engineering 13 (1997) : 583-592.
  • [21] Uddin, M., "RBF-PS scheme for solving the equal width equation", Applied Mathematics and Computation 222 (2013) : 619-631.
  • [22] Dereli, Y., Schaback, R., "The meshless kernel-based method of lines for solving the equal width equation", Applied Mathematics and Computation 219(10) (2013) : 5224-5232.
  • [23] Dhawan, S., Ak, T., Apaydin, G., "Algorithms for numerical solution of the equal width wave equation using multi-quadric quasi-interpolation method", International Journal of Modern Physics C 30(11) (2019) : 1950087.
  • [24] Ghafoor, A., Haq, S., "An efficient numerical scheme for the study of equal width equation", Results in Physics 9 (2018) : 1411-1416.
  • [25] Oruç, Ö., Esen, A., Bulut, F., "Highly accurate numerical scheme based on polynomial scaling functions for equal width equation", Wave Motion 105 (2021) : 102760.
  • [26] Koyulmuş, B., "On high degree B-spline functions", Master thesis, Eskişehir Osmangazi University, Eskişehir, Turkey, 2021 (in Turkish).
Year 2022, , 185 - 194, 30.12.2022
https://doi.org/10.30931/jetas.1072151

Abstract

References

  • [1] Morrison, P.J., Meiss, J.D., Carey, J.R., "Scattering of RLW solitary waves", Physica 11D (1984) : 324-336.
  • [2] Gardner, L.R.T., Gardner, G.A., "Solitary waves of the equal width wave equation", Journal of Computational Physics 101 (1992) : 218-223.
  • [3] Irk, D., "B-Spline Galerkin solutions for the equal width equation", Physics of Wave Phenomena 20(2) (2012) : 122-130.
  • [4] Dağ, İ., Saka, B., Irk, D., "Galerkin method for the numerical solution of the RLW equation using quintic B-splines", Journal of Computational and Applied Mathematics 190 (2006) : 532-547.
  • [5] Saka, B., "A finite element method for equal width equation", Applied Mathematics and Computation 175 (2006) : 730-747.
  • [6] Saka, B., Dag, I., Dereli, Y., Korkmaz, A., "Three different methods for numerical solution of the EW equation", Engineering analysis with boundary elements 32 (2008) : 556-566.
  • [7] Dag, I., Irk, D., Boz, A., "Simulation of EW wave generation via quadratic B-spline finite element method", International Journal of Mathematics and Statistics 1 (A07) (2007) : 46-59.
  • [8] Esen, A., "A numerical solution of the equal width wave equation by a lumped Galerkin method", Applied Mathematics and Computation 168 (2005) : 270-282.
  • [9] Raslan, K.R., "Collocation method using quartic B-spline for the equal width (EW) equation", Applied Mathematics and Computation 168(2) (2005) : 795-805.
  • [10] Dağ, İ., Saka, B., "A cubic B-spline collocation method for the EW equation", Mathematical and Computational Applications 90 (2004) : 381-392.
  • [11] Dag, I., Ersoy, O., "The exponential cubic B-spline algorithm for equal width equation", Advanced Studies in Contemporary Mathematics 25(4) (2015) : 525-535.
  • [12] Yağmurlu, N.M., Karakaş, A.S., "Numerical solutions of the equal width equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization", Numerical Methods for Partial Differential Equations 36(5) (2020) : 1170-1183.
  • [13] Irk, D., Saka, B., Dağ, İ., "Cubic spline collocation method for the equal width equation", Hadronic Journal Supplement 18 (2003) : 201-214.
  • [14] Saka, B., Irk, D., Dağ, İ., "A numerical study of the equal width equation", Hadronic Journal Supplement 18 (2003) : 99-116.
  • [15] Banaja, M.A., Bakodah, H.O., "Runge-Kutta integration of the equal width wave equation using the method of lines", Mathematical Problems in Engineering 2015 (2015) : Article ID 274579.
  • [16] Inan, B., Bahadır, A.R., "A numerical solution of the equal width wave equation using a fully implicit finite difference method", Turkish Journal of Mathematics and Computer Science 2(1) (2014) : 1-14.
  • [17] Zaki, S.I., "A least-squares finite element scheme for the EW equation", Communications in Numerical Methods in Engineering 189 (2000) : 587-594.
  • [18] Doğan, A., "Application of Galerkin's method to equal width wave equation", Applied Mathematics and Computation 160 (2005) : 65-76.
  • [19] Roshan, T., "A Petrov-Galerkin method for equal width equation", Applied Mathematics and Computation 218(6) (2011) : 2730-2739.
  • [20] Gardner, L.R.T., Gardner, G.A., Ayoub, F.A., Amein, N.K., "Simulations of the EW undular bore", Communications in Numerical Methods in Engineering 13 (1997) : 583-592.
  • [21] Uddin, M., "RBF-PS scheme for solving the equal width equation", Applied Mathematics and Computation 222 (2013) : 619-631.
  • [22] Dereli, Y., Schaback, R., "The meshless kernel-based method of lines for solving the equal width equation", Applied Mathematics and Computation 219(10) (2013) : 5224-5232.
  • [23] Dhawan, S., Ak, T., Apaydin, G., "Algorithms for numerical solution of the equal width wave equation using multi-quadric quasi-interpolation method", International Journal of Modern Physics C 30(11) (2019) : 1950087.
  • [24] Ghafoor, A., Haq, S., "An efficient numerical scheme for the study of equal width equation", Results in Physics 9 (2018) : 1411-1416.
  • [25] Oruç, Ö., Esen, A., Bulut, F., "Highly accurate numerical scheme based on polynomial scaling functions for equal width equation", Wave Motion 105 (2021) : 102760.
  • [26] Koyulmuş, B., "On high degree B-spline functions", Master thesis, Eskişehir Osmangazi University, Eskişehir, Turkey, 2021 (in Turkish).
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Melis Zorsahin Gorgulu 0000-0001-7506-4162

Publication Date December 30, 2022
Published in Issue Year 2022

Cite

APA Zorsahin Gorgulu, M. (2022). A New Algorithm Based on the Decic (tenth degree) B-spline Functions for Numerical Solution of the Equal Width Equation. Journal of Engineering Technology and Applied Sciences, 7(3), 185-194. https://doi.org/10.30931/jetas.1072151
AMA Zorsahin Gorgulu M. A New Algorithm Based on the Decic (tenth degree) B-spline Functions for Numerical Solution of the Equal Width Equation. JETAS. December 2022;7(3):185-194. doi:10.30931/jetas.1072151
Chicago Zorsahin Gorgulu, Melis. “A New Algorithm Based on the Decic (tenth Degree) B-Spline Functions for Numerical Solution of the Equal Width Equation”. Journal of Engineering Technology and Applied Sciences 7, no. 3 (December 2022): 185-94. https://doi.org/10.30931/jetas.1072151.
EndNote Zorsahin Gorgulu M (December 1, 2022) A New Algorithm Based on the Decic (tenth degree) B-spline Functions for Numerical Solution of the Equal Width Equation. Journal of Engineering Technology and Applied Sciences 7 3 185–194.
IEEE M. Zorsahin Gorgulu, “A New Algorithm Based on the Decic (tenth degree) B-spline Functions for Numerical Solution of the Equal Width Equation”, JETAS, vol. 7, no. 3, pp. 185–194, 2022, doi: 10.30931/jetas.1072151.
ISNAD Zorsahin Gorgulu, Melis. “A New Algorithm Based on the Decic (tenth Degree) B-Spline Functions for Numerical Solution of the Equal Width Equation”. Journal of Engineering Technology and Applied Sciences 7/3 (December 2022), 185-194. https://doi.org/10.30931/jetas.1072151.
JAMA Zorsahin Gorgulu M. A New Algorithm Based on the Decic (tenth degree) B-spline Functions for Numerical Solution of the Equal Width Equation. JETAS. 2022;7:185–194.
MLA Zorsahin Gorgulu, Melis. “A New Algorithm Based on the Decic (tenth Degree) B-Spline Functions for Numerical Solution of the Equal Width Equation”. Journal of Engineering Technology and Applied Sciences, vol. 7, no. 3, 2022, pp. 185-94, doi:10.30931/jetas.1072151.
Vancouver Zorsahin Gorgulu M. A New Algorithm Based on the Decic (tenth degree) B-spline Functions for Numerical Solution of the Equal Width Equation. JETAS. 2022;7(3):185-94.