Spectral Local Linearisation Approach for Natural Convection Boundary Layer Flow

S. S. Motsa, Z. G. Makukula and S. Shateyi

Mathematical Problems in Engineering, 2013, vol. 2013, 1-7

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:765013

DOI: 10.1155/2013/765013

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