Bernoulli wavelet application to the numerical solution of Jeffery–Hamel flow problem

Abstract

In this study, we introduced the Bernoulli wavelet method (BWM) to address the nonlinear Jeffery–Hamel flow problem. Utilizing a newly devised operational matrix of integration with the Bernoulli wavelet, we apply the Bernoulli wavelet expansion in conjunction with the collocation method to convert the given differential equation into a series of nonlinear equations. These equations are subsequently solved using an appropriate iterative technique. The BWM demonstrates superior accuracy when compared to existing methods like differential transformation, homotopy perturbation, variational iteration, and Runge–Kutta (R–K). Our results indicate the effectiveness of BWM in providing more precise solutions for the Jeffery–Hamel flow, a significant phenomenon with wide applications in various engineering fields, including chemical, aerospace, civil, biomechanical, mechanical, and environmental engineering. The study also delves into the influence of Reynolds number and convergent/divergent channel configurations on Jeffery–Hamel flow applications.