Wavelet solutions of Burgers’ equation with high Reynolds numbers

Abstract

A wavelet method is proposed to solve the Burgers’ equation. Following this method, this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resulting system of ordinary differential equations. Such a wavelet-based solution procedure has been justified by solving two test examples: results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods, and whose order of convergence can go up to 5. Most importantly, our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.