UNIFORM CONVERGENCE OF MONOTONE DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED THIRD-ORDER CONVECTION-DIFFUSION EQUATION

摘要

A singularly perturbed third-order convection-diffusion problem is considered. The third-order boundary value problem is transformed into a system of weakly coupled system of two differential equations. Then the problem is solved numerically using a monotone difference scheme on a Bakhvalov-Shishkin mesh. We use appropriate estimates of the discrete Green's function to obtain error estimates of the monotone difference scheme. Numerical experiments support our theoretical results.