Quartic Trigonometric Tension B-spline Finite Element Method for Solving
Gardner Equation
Abstract
Method of collocation 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 quartic
trigonometric tension 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.