### Higher order splitting approaches in analysis of the Burgers equation

#### Abstract

This article proposes some higher order splitting-up techniques based on cubic B-spline Galerkin finite element method in analysing the Burgers equation model. The strong form of both conservation and diffusion parts of the time-splitted Burgers equation have been considered in building the Galerkin approach. To integrate the corresponding ODE system, the Crank-Nicolson time discretization scheme is used. The proposed schemes are shown to be unconditionally stable. Two challenging examples have been considered with changing values of the kinematic viscosity constant of the medium. Especially, the cases of shock waves of severe gradient are solved and checked with both exact solution and the literature. The qualitative and quantitative results demonstrate that our numerical approach has far higher accuracy than the rival methods.

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