TY - JOUR
T1 - Non-standard Finite Difference Based Numerical Method for Viscous Burgers’ Equation
AU - Clemence, Dominic
AU - Clemence-Mkhope, Dominic P
AU - Rabeeb Ali, V P
AU - Awasthi, Ashish
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
M3 - Article
VL - 6
SP - 154
JO - International Journal of Applied and Computational Mathematics
JF - International Journal of Applied and Computational Mathematics
IS - 6
ER -