On Uniform Difference Schemes of a Higher Order of Approximation for Elliptical Equations with a Small Parameter

Abstract

In a Banach space E we will consider the following boundary value problem for elliptical equations ϵv"(t)=Av(t)+f(t)(0≤t≤1), v(0)=v₀, v(1)=v₁ with a small parameter . For such problem we construct difference schemes of a higher order of approximation which are uniform with respect to the small parameter ϵ

Keywords:

• Uniform difference Schemes
• Elliptical Equations
• Error Estimates
• Coercive inequality