On parameter uniform and layer resolving numerical method for a singularly perturbed model in aerodynamics

Abstract

In this paper, a parameter uniform computational technique is examined for a partially singularly perturbed semi-linear system of equations which models the flight dynamics of an Unmanned Aerial Vehicle (UAV) and a Helicopter. The components of the solution of this system are expected to exhibit overlapping boundary layers at the origin. To resolve the layers, a piecewise uniform Shishkin mesh is constructed so that a half of the mesh points are obtained in the layer region. The numerical method is proved to be parameter uniform and first order convergent. The method is tested for few numerical examples.

Keywords

• System of singularly perturbed equations
• Non-linear control
• UAV model
• Boundary layers
• Shishkin mesh