An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method

TL;DR

This paper introduces a pseudospectral method using Hermite functions to solve the nonlinear Falkner-Skan boundary layer equation on a semi-infinite domain, avoiding domain truncation and transformation.

Contribution

The paper presents a novel pseudospectral approach with Hermite functions for solving semi-infinite domain boundary layer equations, eliminating the need for domain truncation.

Findings

Method accurately solves Falkner-Skan equation

Results agree with existing numerical solutions

Efficiently handles semi-infinite domain without truncation

Abstract

Based on a new approximation method, namely pseudospectral method, a solution for the three order nonlinear ordinary differential laminar boundary layer Falkner-Skan equation has been obtained on the semi-infinite domain. The proposed approach is equipped by the orthogonal Hermite functions that have perfect properties to achieve this goal. This method solves the problem on the semi-infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, this method reduces solution of the problem to solution of a system of algebraic equations. We also present the comparison of this work with numerical results and show that the present method is applicable.