Solving Benjamin-Bona-Mahony equation using besse B-spline relaxation scheme

Abstract

In this research, the Benjamin-Bona-Mahony (BBM) equation is solved numerically using cubic B-spline (CBS) collocation method. The BBM equation is transformed into a system of two equations and Besse’s formula is applied to the nonlinear term. Then, Forward Difference Approximation is used to discretize the time derivative while the CBS function is used to discretize the space dimension. Two numerical examples are discussed and compared with the exact solutions.In this research, the Benjamin-Bona-Mahony (BBM) equation is solved numerically using cubic B-spline (CBS) collocation method. The BBM equation is transformed into a system of two equations and Besse’s formula is applied to the nonlinear term. Then, Forward Difference Approximation is used to discretize the time derivative while the CBS function is used to discretize the space dimension. Two numerical examples are discussed and compared with the exact solutions.