In this paper, an efficient method has been introduced for solving the generalized Burgers’ equation by combining Hermite interpolating polynomials and the nonstandard finite difference technique. Initially, the time derivative is discretized using the nonstandard finite difference method and the spatial derivatives are discretized using a \(\theta -\) weighted scheme. The computation is further based on quintic Hermite polynomials, transforming the differential equations into algebraic equations which are then solved numerically using MATLAB. Stability analysis is conducted using the Von Neumann approach. An adequate investigation has been performed for test problems with higher order nonlinearities for demonstrating the application of the proposed method. The numerical solutions obtained for them closely match the exact solution and give better results than existing literature. The obtained rate of convergence is of nearly third order. This approach can be applied widely to various nonlinear physical models, as it is efficient in terms of easy implementation and high accuracy.
