  In the study, the collocation method based on exponential cubic B-spline
functions is proposed to solve one dimensional Boussinesq systems numerically.
Two initial boundary value problems for Regularized and Classical Boussinesq
systems modeling motion of traveling waves are considered. The accuracy of the
method is validated by measuring the error between the numerical and analytical
solutions. The numerical solutions obtained by various values of free parameter
$p$ are compared with some solutions in literature.
