Approximation of derivative to a singularly perturbed second-order ordinary differential equation with discontinuous convection coefficient using hybrid difference scheme

Abstract

In this paper, a hybrid difference scheme for singularly perturbed second-order ordinary differentialequations with a discontinuous convection coefficient is presented. A parameter-uniform error bound for the numerical derivative is established using hybrid difference scheme on a Shishkin mesh. Numerical results are provided to illustrate the theoretical results.

Keywords:

• singular perturbation problems
• discontinuous convection term
• scaled derivative
• scaled discrete derivative
• hybrid scheme

2000 AMS Subject Classification :

• 65L10
• 65L12
• 65L50
• 65L70
• 34B05
• 34B60

Acknowledgements

The authors would like to thank the referees for their valuable comments. The first author wishes to acknowledge Bharathidasan University, Tamilnadu, India, for its financial support.