Block iterative methods for the numerical solution of three dimensional mildly non-linear biharmonic problems of first kind

In this article, we discuss two sets of new finite difference methods of or der two and four using 19 and 27 grid points, respectively over a cubic dom ain for solving the three dimensional nonlinear elliptic biharmonic problem s of first kind. For both the cases we use block iterative methods and a si ngle computational cell. The numerical solution of (partial derivativeu/par tial derivativen) are obtained as byproduct of the methods and we do not re quire fictitious points in order to approximate the boundary conditions. Th e resulting matrix system is solved by the block iterative method using a t ri-diagonal solver. In numerical experiments the proposed methods are compa red with the exact solutions both in singular and non-singular cases.