Solving Boussinesq equation using quintic B-spline and quintic trigonometric B-spline interpolation methods

A new quintic B-spline approximation for numerical treatment of Boussinesq equation

“…The computational error norms L 2 and L ∞ corresponding to different time stages are reported in Table 2 by setting 0 x 10, 0 t 0.1, λ = 1.116, and ∆t = 0.01. The approximate results are found to be better than QnTBSM [25]. The one dimensional plots of exact and approximate solutions are shown in Figure 3 using −10 x 15, t = 1, 2, 3, 4, 5, λ = 1.116, and ∆t = 0.01.…”

“…where U i and u i represent the numerical and exact solutions at the i th knot, respectively. The computational outcomes are compared with those obtained by quintic B-spline collocation method (QnBSM) [20] and quintic trigonometric B-spline collocation method (QnTBSM) [25]. Problem 7.1.…”

“…Figure 4 exhibits the 3D plots of approximate and analytical exact solution when −10 x 15, 0 t 1, λ = 1.116, and ∆t = 0.01. QnTBS [25] Proposed method t L 2 L ∞ L 2 L ∞ 0.02 1.01 × 10 −3 5.20 × 10 −4 1.66 × 10 −6 9.73 × 10 −7 0.04 2.05 × 10 −3 1.05 × 10 −3 7.30 × 10 −6 5.55 × 10 −6 0.06 3.12 × 10 −3 1.59 × 10 −3 1.73 × 10…”

“…It describes several physical phenomena such as propagation of waves, non-linear plasma waves exhibiting some dissipative effects, propagation of bores and wave diffraction in shallow waters [9,14,15]. The shallow water wave equations have several applications including storm and Tsunami propagation, river flooding and dam breaks [25]. The generalized BE is given by…”

“…The authors in [18] employed homotopy analysis method (HAM) to explore the analytical solution of BE with variable coefficients. Zakaria et al [25] used quintic trigonometric B-spline collocation method (QnTBSM) to study the numerical solution of BE. Jang [16] introduced a new semi analytic dispersion-relation preserving method to integrate the Boussinesq like equations.…”