A fast and accurate computational technique for efficient numerical solution of nonlinear singular boundary value problems

ABSTRACT

This paper is concerned with design and implementation of a computational technique for the efficient solution of a class of singular boundary value problems. The method is based on a modified homotopy analysis method. The method is illustrated by six examples, two of which arise in chemical engineering: the first problem arises in the study of thermal explosions, while the second problem arises in the study of heat and mass transfer within the porous catalyst particles. Numerical results reveal that our method provides better results as compared to some existing methods. Furthermore, it is a powerful tool for dealing with different types of problems with strong nonlinearity.

Keywords:

• Singular two-point boundary value problems
• homotopy analysis method
• Heat and mass transfer problem
• thermal explosion problem
• heat conduction problem
• physiological problem

2010 AMS SUBJECT CLASSIFICATIONS:

• 34B05
• 34B15
• 34B16
• 34B60

Acknowledgements

The author is very grateful to the Editor-in-Chief and anonymous referees for their valuable suggestions and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Science and Engineering Research Board, DST, India (SB/S4/MS/877/2014).