A new high accuracy method in exponential form based on off-step discretization for non-linear two point boundary value problems

ABSTRACT

This paper is intended to describe a graded mesh implicit method based upon half step discretization of order three for the solution of non-linear two point boundary value problem of the form $u^{\mathrm{\prime }\mathrm{\prime }}=f(x,u,u^{\mathrm{\prime }})$, $x\in (a,b)$. The devised method is compact and uses three nodal points for the unknown function u(x) and two nodal points for the known variable ‘x’ in spatial axis. A detailed convergence analysis has also been included. This method, though meant for scalar equations was further extended to compute the vector equations of two point nonlinear boundary value problems. The method is directly applicable to singular problems. Computational results are provided to assess the performance and reliability of the method.

KEYWORDS:

• Exponentially fitted
• study of convergence
• Burger's equation
• convection-diffusion equation
• modified Emden equation
• Vanderpol's equation
• Duffing equation
• off-step points

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65L10
• 65L12
• 65L20

Acknowledgements

The authors thank the reviewes for their valuable suggestions which substantially improved the standard of the paper. This work is supported by Maitreyi College, University of Delhi, India.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

R. K. Mohanty http://orcid.org/0000-0001-6832-1239

Geetan Manchanda http://orcid.org/0000-0003-0785-4909

Arshad Khan http://orcid.org/0000-0003-3783-188X

Gunjan Khurana http://orcid.org/0000-0002-0634-6577