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Efficient numerical techniques for Burgers’ equation

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  • Mukundan, Vijitha
  • Awasthi, Ashish

Abstract

This paper presents new efficient numerical techniques for solving one dimensional quasi-linear Burgers’ equation. Burgers’ equation is used as a model problem in the study of turbulence, boundary layer behavior, shock waves, convection dominated diffusion phenomena, gas dynamics, acoustic attenuation in fog and continuum traffic simulation. Using a non-linear Cole–Hopf transformation the Burgers’ equation is reduced to one-dimensional diffusion equation. The linearized diffusion equation is semi discretized by using method of lines (MOL) which leads to a system of ordinary differential equations in time. Resulting system of ordinary differential equations is solved by backward differentiation formulas (BDF) of order one, two and three and the analysis of numerical errors are presented. Numerical results for modest values of kinematic viscosity are compared with the exact solution to demonstrate the efficiency of proposed numerical methods.

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  • Mukundan, Vijitha & Awasthi, Ashish, 2015. "Efficient numerical techniques for Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 282-297.
    • Handle: RePEc:eee:apmaco:v:262:y:2015:i:c:p:282-297
    DOI: 10.1016/j.amc.2015.03.122
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    Cited by:

    1. Guo, Yan & Shi, Yu-feng & Li, Yi-min, 2016. "A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 172-185.
    2. Muaz Seydaoğlu, 2019. "A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
    3. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    4. Chen, Changkai & Zhang, Xiaohua & Liu, Zhang, 2020. "A high-order compact finite difference scheme and precise integration method based on modified Hopf-Cole transformation for numerical simulation of n-dimensional Burgers’ system," Applied Mathematics and Computation, Elsevier, vol. 372(C).

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