Numerical solutions of Boussinesq equation using Galerkin finite element method

In this study, Galerkin finite element method has been applied to good Boussinesq (GBq) and bad Boussinesq (BBq) equations which are examples of Boussinesq type equations. To apply the method, cubic B-spline basis functions are taken as element and weight functions. The solutions of the numerical schemes have been obtained using the fourth order Runge-Kutta method. The error norms L-2 and L-infinity have been used to test how compatible they obtained numerical solutions with those of exact ones. As numerical examples, solitary wave motion and interaction of solitary waves have been investigated for both GBq and BBq equation. Also blow-up solutions related to the interaction of two solitary waves are considered for GBq equation.

Automated summary

In this study, the Galerkin finite element method was applied to solve the good and bad Boussinesq equations, providing numerical solutions. The fourth order Runge-Kutta method was used to obtain numerical solutions, and error norms were used to test the accuracy of the solutions. The research investigated solitary wave motion, interaction of solitary waves, and blow-up solutions related to the interaction of two solitary waves.