A quartic trigonometric tension B‐spline finite element method for solving Gardner equation

Abstract

The collocation method is established for getting solution of the Gardner equation (GE). The GE is fully integrated by way of the Crank-Nicolson method for time variable and collocation method for spatial variable. Trial function of the collocation method is set up using combination of quartic trigonometric tension (QTT) B-splines. Convergence analysis of suggested method is investigated. Performance of the QTT B-splines is searched by studying three test problems: propagation of bell shape solitary wave, interaction of two positive bell shape solitary wave and wave generation.