Analysis of MHD boundary layer flow of a viscous fluid past a stretching sheet employing the Legendre wavelet method

The current work introduces a novel approach to analyse the non-linear Falkner–Skan equation from fluid dynamics by utilising the Legendre wavelet method. In this paper, we relied on the Legendre wavelet to generate a new functional integration matrix and presented a novel approach known as the Legendre wavelet approach (LWA). The primary goal of this study is to provide a unified method via LWA to compute an approximate solution to a non-linear differential equation for a viscous fluid over a stretching sheet. The Legendre wavelet method has been used for the first time to solve the stretching sheet problem. A viscous fluid across a stretching sheet has been explored for its stable laminar magnetohydrodynamic (MHD) flow, transportation of mass and heat characteristics in the context of an intermittent magnetic field. By specifying appropriate non-dimensional parameters, the governing boundary layer equation evolves into a dimension devoid of the Falkner–Skan equation. Using the Legendre wavelet approach, the resulting nonlinear equation modified to an algebraic equation is addressed. With LWA, the undershoots and overshoots for a set of factors are noted. The boundary layer thickness appears to decrease with increasing pressure gradient and magnetic field parameters. The graphical interpretation of the boundary layer flow’s features is done for a range of physical parameter values. To ensure the accuracy of the findings, local skin friction has been tracked and contrasted with other techniques that are already documented in the previous research. © 2024 Informa UK Limited, trading as Taylor & Francis Group.