In this paper, we propose two efficient algorithms based on Broyden's methods by using the central finite difference and modification of Newton's method for solving systems of nonlinear equations. The most significant features of these algorithms are their simplicity and excellent accuracy. Some numerical examples are given to test the validity of the proposed algorithms and for comparison reasons. Superior results show the efficiency and accuracy of the proposed algorithms and a tremendous improvements in Broyden's methods.

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In this paper, we present parallel implementation of the Gauss-Seidel (GS) iterative algorithm for the solution of linear systems of equations on a k-ary n-cube parallel machine using Open MPI as a parallel programming environment. The proposed algorithm is of O(N

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In this paper, we propose an algorithm using the cubic spline interpolation on the fi nite diff erence method to solve the Bratu-type equation. The algorithm has been successfully implemented. Numerical results are also given to demonstrate the validity and the applicability of the proposed algorithm. The results we obtained show that the proposed algorithm perform better than some existing methods in the literature.

In this paper, we develop and evaluate a parallel algorithm for GESPP on a cluster of Silicon Graphics workstations using PVM as a parallel programming environment. The proposed algorithm reduces the computation time to O and the communication time to including scaling, searching for the pivot element, row interchanging, and pivot row and multipliers column broadcasting. The numerical experiments show that the proposed parallel algorithm offers a high speedup and efficiency for the test problems. ) / ( 3 p n ) (n O

Network-on-chip multicore architectures with a large number of processing elements are becoming a reality with the recent developments in technology. In these modern systems the processing elements are interconnected with regular network-on-chip (NoC) topologies such as meshes and trees. In this paper we propose a parallel Gauss-Seidel (GS) iterative algorithm for solving large systems of linear equations on a torus NoC architecture. The proposed parallel algorithm is O (Nn2/k2) time complexity for solving a system with matrix of order n on a k × k torus NoC architecture with N iterations assuming n and N are large compared to k (i.e. for large linear systems that require a large number of iterations). We show that under these conditions the proposed parallel GS algorithm has near optimal speedup.

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