Finite difference methods of order two and four for 2-D non-linear biharmonic problems of first kind

Abstract

For the numerical integration of the 2-D nonlinear biharmonic problems of first kind, we report two difference methods of order two and four over a rectangular domain. These methods use only the nine grid points and do not require fictitious points in order to approximate the boundary conditions. Derivatives of the solution are obtained as a by-product of the methods. In numerical experiments, the new second and fourth order formulas are compared with the exact solutions.