Abstract
Simple and accurate non-standard finite difference (NSFD) schemes are proposed for solving the viscous Burgers’ equation with and without Cole–Hopf transformation. The stability and positivity of the schemes are discussed in detail, and the schemes are very user friendly in implementation. For some classic examples for the viscous Burgers’ equation, simulation outcomes are validated through comparison with exact solutions for small and large values of kinematic viscosity. Numerical results from the NSFD schemes and corresponding standard finite difference methods are tabulated and compared with results from some existing methods. The proposed schemes give relatively accurate results, with comparatively less observed absolute errors.
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