Fitted mesh method for singularly perturbed fourth order differential equation of convection diffusion type with integral boundary condition

Abstract

This article focuses on a class of fourth-order singularly perturbed convection diffusion equations (SPCDE) with integral boundary conditions (IBC). A numerical method based on a finite difference scheme using Shishkin mesh is presented. The proposed method is close to the first-order convergent. The discrete norm yields an error estimate and theoretical estimations are tested by numerical experiments.

Keywords

• fourth order differential equation
• non-local boundary condition
• finite difference scheme
• singular perturbation problems
• shishkin mesh