Spectral Local Linearisation Approach for Natural Convection Boundary Layer Flow

Abstract EN

The present work introduces a spectral local linearisation method (SLLM) to solve a natural convection boundary layer flow problem with domain transformation.

It is customary to find solutions of semi-infinite interval problems by first truncating the interval and subsequently applying a suitable numerical method.

However, this gives rise to increased error terms in the numerical solution.

Carrying out a transformation of the semi-infinite interval problems into singular problems posed on a finite interval can avoid the domain truncation error and enables the efficient application of collocation methods.

The SLLM is based on linearising and decoupling nonlinear systems of equations into a sequence or subsystems of differential equations which are then solved using spectral collocation methods.

A comparative study between the SLLM and existing results in the literature was carried out to validate the results.

The method has shown to be a promising efficient tool for nonlinear boundary value problems as it gives converging results after very few iterations.