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.