An Efficient Non-Standard Numerical Scheme Coupled with a Compact Finite Difference Method to Solve the One-Dimensional Burgers’ Equation

This article proposes a family of non-standard methods coupled with compact finite differences to numerically integrate the non-linear Burgers’ equation. Firstly, is derived deal system ordinary differential equations (ODEs) arising from semi-discretization initial-boundary value partial (PDEs). Further, method this considered as special case and fourth-order difference resulting in combined numerical scheme solve PDEs. The has first-order accuracy time space. Some basic characteristics are analysed section concerning experiments presented demonstrating good performance scheme.