A fourth-order finite difference method for the general one-dimensional nonlinear biharmonic problems of first kind
This paper derives a fourth-order difference scheme for fourth-order boundary value problems subject to natural boundary conditions based on only three grid points. The ensuring coupled block systems can be solved iteratively by block successive overrelaxation (either linearly or nonlinearly depending on the differential equation). Convergence properties of these iterations are studied analytically for a model linear problem and numerical results are presented. There are issues associated with convergence and loss of order due to roundoff errors.
scientific article; zbMATH DE number 1419821