Block iterative methods for the numerical solution of two dimensional nonlinear biharmonic equations

Abstract

Block iterative methods are proposed for solving the biharmonic equation using finite difference methods of order two and four over a square domain. For both the cases, we use nine grid points. Derivatives of the solutions are obtained as a 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. Numerical examples are provided to demonstrate the efficiency and accuracy of the methods discussed.