Numerical study of wave disturbances of the high order nonlinear Boussinesq equations arising in engineering

Wave prediction has remained a major challenge for scientists in coastal regions for many years. Damage to infrastructure as well as individuals in coastal locations is often caused by wave modification. In order to obtain physical effects, an accurate numerical simulation of wave disturbances within bathymetry must take into account both dispersive and nonlinear waves. In this study, a quintic trigonometric B-spline (QTBS) can give smoother transitions and more accurate estimates for certain kinds of data because of their trigonometric basis. They retain the local control property of standard B-splines while potentially providing superior smoothness and curve control. A QTBS is presented to generate the numerical solutions for nonlinear Boussinesq equation (BE). The finite difference (FD) formulation is applied for temporal derivative and the QTBS functions for space side with \(\theta \) $\theta$ -weighted scheme. Furthermore, the existence and uniqueness of the solution to the nonlinear BE is also provided. The proposed technique is unconditionally stable for the range of \(\theta \in [1/2, 1]\) $\theta \in [1/2,1]$ . The results of numerical examples have been analyzed with the published results and exact solution to present the effectiveness of the technique computationally and graphically.