Sensitivity analysis of shock wave Burgers’ equation via a novel algorithm based on scale-3 Haar wavelets

ABSTRACT

In this paper, a novel technique is being formulated for the numerical solutions of Shock wave Burgers' equations for planar and non-planar geometry. It is well known that Burgers' equation is sensitive to the perturbations in the diffusion term. Thus we use robustness of wavelets generated by dilation and translation of Haar wavelets on third scale to capture the sensitivity information. The present approach is an improved form of the scale-2 Haar wavelet method. The scheme is based on the forward finite difference scheme for time integration, scale-3 Haar wavelets for space integration and the nonlinearity has been tackled via quasilinearzation technique. Through scale-3 Haar wavelet analysis once the wavelet coefficient is calculated then we can compute the solutions at near the perturbation point. The computation cost of the present scheme is negligible. The proposed method is tested on six test problems to check its computational efficiency where the convergence analysis of scale-3 Haar wavelet method is the proof of our computational arguments.

KEYWORDS:

• Viscous Burgers’ equations
• scale-3 Haar wavelets
• shock waves
• quasilinearization process
• forward finite difference
• collocation points

2010 AMS SUBJECT CLASSIFICATION:

• 65R10

Additional information

Funding

The work is supported by Science and Engineering Research Board (SERB) under the National Postdoctal Fellowship scheme with grant No. [PDF/2016/000726].