An optimized hybrid block method for solving nonlinear singularly perturbed problems using non-uniform Jain-type meshes

Abstract

This work aims to implement a one-step block method with three optimized hybrid points for solving singularly perturbed nonlinear initial value problems on non-uniform meshes. The basic properties of the method are investigated and it is shown that the proposed method is consistent, zero-stable, convergent and has a large region of absolute stability. The presented numerical results confirm the efficiency and accuracy of the proposed method.

Keywords:

• Singularly perturbed inital value problems
• block method
• zero-stability
• consistency
• non-uniform mesh

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65L04
• 65L11
• 65L20
• 65L50

Disclosure statement

No potential conflict of interest was reported by the author(s).