小参数在高阶导数项的椭圆型方程第一边值问题的一致收敛差分格式

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Uniformly Convergent Difference Schemes for First Boundary Value Problem for Elliptic Differential Equations with a Small Parameter at the Highest Derivative

摘要: 本文讨论了曲边区域上小参数ε在高阶导数项的椭圆型方程第一边值问题,从一致收敛的必要条件出发构造了特殊的差分格式,证明了差分方程问题解的一致收敛性,估计了收敛的阶数,并讨论了差分方程解的渐近性态.

Abstract: In this paper we consider the Dirichlet problem for elliptic differential equations. A special difference scheme is constructed from the necessary condition of uniform convergence. We also prove the uniform convergence and the asymptotic behavior of the solution of the difference problem, and give the error estimate.

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