Solving Boussinesq equation using quintic B-spline and quintic trigonometric B-spline interpolation methods

Abstract

The quintic B-spline (QBS) and quintic trigonometric B-spline (QTBS) functions are used to set up the collocation methods in finding solutions for the Boussinesq equation. The QBS and QTBS are applied as interpolating functions in the spatial dimension while the finite difference method (FDM) is used to discretize the time derivative. The nonlinear Boussinesq equation is linearized using Taylor's expansion. The von Neumann stability analysis is used to analyze the schemes and they are shown to be conditionally stable. In order to demonstrate the capability of the schemes, some problems are solved and compared with the analytical solutions and generated results from the FDM. The proposed numerical schemes are found to be accurate.