A computational method for nonlinear Burgers' equation using quartic-trigonometric tension B-splines

Abstract

This work proposes a finite element method emphasizing with quartic-trigonometric basis functions for finding the numerical solution of nonlinear Burgers' equation. The computational scheme is constructed by a discretized space-time hybrid approach using B-spline functions. This methodology produces a system of time-dependent differential equations which is integrated by finite elements technique. The experimental cases including graphical patterns of each wave interaction are simulated by the current computational algorithm. In addition, the method establishes the capacity to provide highly efficient solutions with relative ease of computation. Investigation of the stability analysis shows that the current computational method serves an unconditional stable numerical scheme.