Semi–analytical and numerical simulations of the modified Benjamin–Bona–Mahony model

In this article, semi-analytical and numerical simulations of the well-known modified Benjamin–Bona–Mahony (mBBM) equation are processed. This study targets to check the accuracy of the obtained analytical solutions of the mBBM model that have been obtained in [1] through three recent analytical schemes (extended simplest equation (ESE) method, modified kudryashov (mKud) method, and Sech-Tanh (ST) expansion method). The considered model describes the propagation of long waves in the nonlinear dispersive media in a visual illusion. The Homotopy iteration (HI) method, exponential cubic - B-spline (ECBS) method, and trigonometric- quantic-B-spline (TQBS) method are employed to construct novel semi-analytical and accurate numerical solutions. The obtained solutions’ accuracy has been checked through some different types of two-dimensional graphs