BLOCK ITERATIVE METHODS FOR ONE DIMENSIONAL NONLINEAR BIHARMONIC PROBLEMS ON A PARALLEL COMPUTER*

* Supported by Department of Science and Technology. Government of India under the BOYSCAST fellowship programme.

Abstract

In this article, we propose new difference methods of order two and four using three grid points in a coupled manner for solving the one dimensional nonlinear biharmonic problems with specified boundary conditions at the end points. The resulting matrix system is solved by the block iterative methods on a parallel computer. Derivatives of the solution are obtained as a by-product of the methods. Numerical examples are provided to demonstrate the efficiency and accuracy of the methods on both sequential and parallel computations.

Keywords:

• Biharmonic problems
• Finite difference method
• Block iterative methods
• NBSOR method
• BSOR method
• Parallel computations

Notes

* Supported by Department of Science and Technology. Government of India under the BOYSCAST fellowship programme.

‡ Dept. of Computing, Nottingham Trent University, U.K.