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Conjugate Gradient Method with Ritz Method for the Solution of Boundary Value Problems

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Author(s): Victor Onomza WAZIRI | Kayode Rufus ADEBOYE

Journal: Leonardo Electronic Journal of Practices and Technologies
ISSN 1583-1078

Volume: 6;
Issue: 10;
Start page: 67;
Date: 2007;
Original page

Keywords: Conjugate gradient method (CGM) | Extended conjugate gradient method (ECGM) | Optimal control | Boundary values problem (BVP) | Ritz algorithm | Variational method

ABSTRACT
In this paper, we wish to determine the optimal control of a one-variable boundary value problem using the Ritz algorithm. The posed optimal control problem was inadequate to achieve our goal using the Conjugate Gradient Method version developed by (Harsdoff, 1976). It is anticipated that other operators from some given different problems may sustain the application of the algorithm if the approximate solutions terms are properly chosen quadratic functionals. The graphical solution given at the end of section five of the paper, however, shows that our problem can not have an optimal minimum value since the minimum output is not unique. The optimal value obtained using Mathcad program codes may constitute a conjugate gradient approximate numerical value. As observed from the graphical output, Ritz algorithm could give credence for wider horizon in the engineering computational methods for vibrations of mechanical components and simulates.
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