An Iterative Transformation Method for a Similarity Boundary Layer Model

TL;DR

This paper introduces an iterative transformation method based on scaling invariance theory to numerically solve a similarity boundary layer model, effectively handling a parameter-dependent boundary value problem on a semi-infinite interval.

Contribution

The paper presents a novel iterative transformation approach for solving parameter-dependent boundary layer problems with improved accuracy and efficiency.

Findings

Successfully solves the boundary layer model for a wide parameter range.

Achieves high accuracy compared to known exact solutions.

Demonstrates the method's effectiveness on semi-infinite interval problems.

Abstract

In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is defined on a semi-infinite interval. Using our transformation method we are able to solve the problem in point for a large range of the parameter involved. As far as the accuracy of our numerical method is concerned, for two specific values of the involved parameter, we are able to compare favorably the obtained numerical result for the so-called missing initial condition to the exact solution reported by Crane [Z. Angew. Math. Phys., 21:645-647, 1970].