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.
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