The Physical Model and Numerical Investigation of B‐Equations Based on Quintic Trigonometric B‐Spline Collocation Technique with Finite Difference and Crank‐Nicolson Schemes

In order to construct physical models of B‐equations, such as nonlinear Camassa–Holm (CH), modified Camassa–Holm (MCH), Degasperis–Procesi (DP), and modified Degasperis–Procesi (MDP) equations that arise in shallow water waves, this paper provides a quintic trigonometric B‐spline function based on collocation and a finite difference scheme. For the spatial and temporal derivatives, discretization is accomplished using the trigonometric B‐spline function of degree five and the finite difference technique, respectively. The approximate results are contrasted with the analytical results and other published methods in the literature. Furthermore, it is demonstrated that the method is unconditionally stable with the von Neumann method and accurate to convergence with order . Four representative examples are provided to show the benefit of the suggested method. For some current physical difficulties, the suggested procedure is considered to be a very reliable alternative.