Numerical Analysis of a Benjamin–Bona–Mahony Type Equation in a Noncylindrical Domain

ABSTRACT Numerical analysis and simulation for the approximate solution of a Benjamin–Bona–Mahony type equation defined in a noncylindrical domain are presented in this article. The approximate problem is defined using the linearized Crank–Nicolson Galerkin method, which results in a linear algebraic system at each time step while maintaining quadratic convergence order in time. Numerical simulations and tables are displayed to illustrate the convergence order in both time and space for different types of moving boundaries. These results justify the consistency between theoretical analysis and numerical simulations, validating the precision, stability, and applicability of the proposed numerical method.