| Abstract: | In this article, we discuss two sets of new finite difference methods of order two and four using 19 and 27 grid points, respectively over a cubic domain for solving the three dimensional nonlinear elliptic biharmonic problems of first kind. For both the cases we use block iterative methods and a single computational cell. The numerical solution of (?u/?n) are obtained as by-product of the methods and we do not require fictitious points in order to approximate the boundary conditions. The resulting matrix system is solved by the block iterative method using a tri-diagonal solver. In numerical experiments the proposed methods are compared with the exact solutions both in singular and non-singular cases. |
