Uniformly convergent difference schemes for a first boundary value problem for elliptic differential equations with a small parameter at the highest derivative
The Dirichlet problem for the elliptic equation \[ \partial^ 2u/\partial x^ 2+\epsilon \partial^ 2u/\partial y^ 2+a\partial u/\partial x-b\partial u/\partial y-cu=f \] with a small parameter \(\epsilon >b\) is considered in the case of a region \(\Omega =\{(x,y)| \quad y_ 0\leq y\leq y^ 0\gamma_ 1(y)\leq x\leq \gamma_ 2(y)\}.\) A necessary condition for the uniform convergence of difference schemes is discussed and a special scheme with uniform convergence is suggested.
scientific article; zbMATH DE number 4030887