Novel Transparent Boundary Conditions for the Regularized Long Wave Equation

Abstract

In this paper, we present a new method to derive transparent boundary conditions for the Regularized Long Wave equation and its linearized equation. These boundary conditions have the advantage of being exact for both linearized and nonlinear equations. The resulting problems supplemented with initial data are approximated numerically using finite difference method in space discretization and Crank–Nicolson scheme in time for the linearized equation, while implicit scheme in time is used for the Regularized Long Wave equation. Numerical experiments are made for solitary initial data and various source terms to illustrate the transparency of the introduced boundary conditions. Results are compared with the use of usual boundary conditions, namely, Dirichlet and Neumann via infinite norm error on the boundary and also by displaying geophones and instantaneous figures.