Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations

Abstract

In this paper, we consider a singularly perturbed boundary-value problem for fourth-order ordinary differential equation (ODE) whose highest-order derivative is multiplied by a small perturbation parameter. To solve this ODE, we transform the differential equation into a coupled system of two singularly perturbed ODEs. The classical central difference scheme is used to discretize the system of ODEs on a nonuniform mesh which is generated by equidistribution of a positive monitor function. We have shown that the proposed technique provides first-order accuracy independent of the perturbation parameter. Numerical experiments are provided to validate the theoretical results.

Keywords:

• singularly perturbed boundary-value problems
• boundary layers
• fourth-order ODE
• grid equidistribution
• adaptively generated mesh
• uniform convergence

2010 AMS Subject Classification:

• 65L10

ACM Computing Classification System Code:

• G.1.7

Acknowledgements

The authors express their sincere thanks to the referees for their valuable suggestions.