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

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

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.

___

  • [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).