High-order finite difference schemes for the solution of second-order BVPs
The paper is (mainly) concerned with two-point Dirichlet boundary value problems (BVPs) for second-order ordinary differential equations. The authors propose higher-order generalizations of classical finite difference schemes for their numerical solution. For this purpose, more than just direct neighbours are incorporated into the approximating formulas. A simple linear problem serves for analyzing the condition of the resulting matrix. Two numerical examples illustrate the quality of the proposed methods. Finally, a short proposal refers to applications to elliptic boundary value problems.
scientific article; zbMATH DE number 2137363