Shock Waves Analysis Of Planar And Non Planar Nonlinear Burgers\u27 Equation Using Scale-2 Haar Wavelets

Purpose - This paper aims to find the numerical solution of planar and non-planar Burgers\u27 equation and analysis of the shock behave. Design/methodology/approach - First, the authors discritize the time-dependent term using Crank-Nicholson finite difference approximation and use quasilinearization to linearize the nonlinear term then apply Scale-2 Haar wavelets for space integration. After applying this scheme on partial differential, the equation transforms into a system of algebraic equation. Then, the system of equation is solved using Gauss elimination method. Findings - Present method is the extension of the method (Jiwari, 2012). The numerical solutions using Scale-2 Haar wavelets prove that the proposed method is reliable for planar and non-planar nonlinear Burgers\u27 equation and yields results better than other methods and compatible with the exact solutions. Originality/value - The numerical results for non-planar Burgers\u27 equation are very sparse. In the present paper, the authors identify where the shock wave and discontinuity occur in planar and non-planar Burgers\u27 equation