Solitary wave simulations of the Boussinesq Systems
This is an incremental improvement in numerical methods for solving Boussinesq systems, relevant to researchers in computational fluid dynamics and wave modeling.
The paper proposes a collocation method using exponential cubic B-spline functions to numerically solve one-dimensional Boussinesq systems for solitary wave simulations. The method's accuracy is validated by comparing numerical and analytical solutions, and results for different free parameter values are compared with existing literature.
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.