Quantum mechanics

Neuroscience

Biology

Optical illusion

Boundary value problem

Applied mathematics

Hamiltonian system

Convergence (economics)

Economics

Mathematical optimization

Hamiltonian (control theory)

Physics

Nonlinear system

Mathematics

Mathematical analysis

Geometry

Economic growth

Illusion

Alexandria Engineering Journal

This research is based on three main pillars which are studying the computational solutions of the modified Benjamin–Bona–Mahony (BBM) equation via the modified Khater method then investigating the stability property of the obtained solutions through the Hamiltonian system’s features, evaluating the initial and boundary conditions that allow applying the B-spline collection schemes (cubic, quantic, septic) to find the numerical solutions of the suggested model and to explain the matching between our obtained types of solutions. This model is used in the optical illusions field by describing the propagation of long waves in the nonlinear dispersive media in a visual illusion. An optical illusion is an illusion caused by the visual system and characterized. Four distinct types of sketches (2D, 3D, contour, and Stream plots) have been employed for better understanding our obtained solutions and their convergence.

Novel computational and accurate numerical solutions of the modified Benjamin–Bona–Mahony (BBM) equation arising in the optical illusions field