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Research ArticleOpen accessPhrase in the titleParallel Approaches for Intervals Analysis of Variable Statistics in Large and Sparse Linear Equations with RHS RangesPeerayuth CharnsethikulThis study proposes an algorithm capable of working in parallel for solving large and sparse linear equations under given right hand side (RHS) ranges. A comparative study to the direct linear programming method is reported theoretically, computationally and discussed. Moreover, the approach can be adapted for the system under domain decompositions structure leading to a better efficiency experimentally. …American Journal of Applied Sciences, Vol. 4, Issue 5 · 31 May 2007 · 6,823 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleA New Newton's Method with Diagonal Jacobian Approximation for Systems of Nonlinear EquationsM. Y. Waziri, W. J. Leong, M. A. Hassan, M. MonsiProblem statement: The major weaknesses of Newton method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in each of the iterations. Approach: In some extent function derivatives are quit costly and Jacobian is computationally expensive which requires evaluation (storage) of n×n matrix in every iteration. Results: This storage requirement became unrealistic when n … …Journal of Mathematics and Statistics, Vol. 6, Issue 3 · 30 Sep 2010 · 8,538 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn the Pseudo-Spectral Method of Solving Linear Ordinary Differential EquationsB. S. OgundareProblem statement: Not all differential equations can be solved analytically, to overcome this problem, there is need to search for an accurate approximate solution. Approach: The objective of this study was to find an accurate approximation technique (scheme) for solving linear differential equations. By exploiting the Trigonometric identity property of the Chebyshev polynomial, we developed a numerical scheme referred to … …Journal of Mathematics and Statistics, Vol. 5, Issue 2 · 30 Jun 2009 · 7,222 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn the Closed Form Solutions of Linear and Nonlinear Cauchy Reaction-Diffusion Equations Using the Hybrid of Fourier Transform and Variational Iteration MethodS.S. Nourazar, A. Nazari-Golshan, M. NourazarProblem statement: In the present study, a hybrid of Fourier transform and Variational Iteration Method (FTVIM) is developed for solving the non-homogeneous linear and nonlinear partial differential equations of Cauchy reaction-diffusion problem. Approach: The closed form solutions obtained from the series solution of recursive sequences is valid for the entire range of problem domain. Results and Conclusion: Moreover, the very … …Physics International, Vol. 2, Issue 1 · 26 Oct 2011 · 8,195 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleCost Analysis of Two-Dissimilar-Unit Cold Standby System with three States and Preventive Maintenance Using Linear First Order Differential EquationsM. Y. HaggagProblem statement: Several researchers have studied the reliability behavior of a three state systems, but no attention was paid to the reliability evaluation due to preventive maintenance. The better maintenance of the system originates better reliability. Also, standby support increases the reliability of the system. Approach: Determine the efficacy of preventive maintenance on the reliability and performance of the system. … …Journal of Mathematics and Statistics, Vol. 5, Issue 4 · 31 Dec 2009 · 6,873 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleNumerical Solution of Linear Integro-Differential EquationsHusein Jaradat, Omar Alsayyed, S. Al-SharaProblem Statement: Integro-differential equations find special applicability within scientific and mathematical disciplines. In this study, an analytical scheme for solving Integrodifferential equations was presented. Approach: We employed the Homotopy Analysis Method (HAM) to solve linear Fredholm integro-differential equations. Results: Error analysis and illustrative examples were included to demonstrate the validity and applicability of the technique. MATLAB 7 was used to … …Journal of Mathematics and Statistics, Vol. 4, Issue 4 · 31 Dec 2008 · 7,093 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleEvaluation of Reliability and Availability Characteristics of Two Different Systems by Using Linear First Order Differential EquationsKhaled M. El-Said, Mohamed S. EL-SherbenyThis study deals with the reliability and availability characteristics of two different series system configurations. The second system differs from the first system due to the additional feature of preventive maintenance. The failure times of a components are assumed to be exponentially distributed with parameters α,β,α' and β', respectively. The replacement time distribution of each server is also exponentially distributed … …Journal of Mathematics and Statistics, Vol. 1, Issue 2 · 30 Jun 2005 · 6,659 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleNumerical Solution of Fourth Order Linear Ordinary Differential Equations by Cubic Spline Collocation Tau MethodO.A. Taiwo, O.M. OgunlaranProblem Statement: Many boundary value problems that arise in real life situations defy analytical solution; hence numerical techniques are desirable to find the solution of such equations. New numerical methods which are comparatively better than the existing ones in terms of efficiency, accuracy, stability, convergence and computational cost are always needed. Approach: In this study, we developed and applied three … …Journal of Mathematics and Statistics, Vol. 4, Issue 4 · 31 Dec 2008 · 6,985 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph ColoringHaridas Kumar Das, Nasim RezaThis paper is based on the analytic and computational solution procedures of Gröbner basis and its applications. We show the behavior of the ideals generated by polynomials from a polynomial ring. We also present the idea of a zero dimensional ideal and use of this ideal to solve system of polynomial equations. We then introduce an algorithmic procedure for solving … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 27 Jun 2018 · 8,591 accessesView PDFCite
Research ArticleOpen accessIn the keywordsA Computational Method Based on Bernstein Polynomials for Solving FredholmIntegro-Differential Equations under Mixed ConditionsMiloud Moussai, Lakhdar ChiterIn this study, a computational method for solving linear FredholmIntegro-Differential Equation (FIDE) of the first order under the mixed conditions using the Bernstein polynomials. First, we present some properties of these polynomials and the method is explained. These properties are then used to convert the integro-differential equation to a system of linear algebraic equations with unknown Bernstein coefficients. Using Galerkin … …Journal of Mathematics and Statistics, Vol. 13, Issue 1 · 27 Feb 2017 · 7,142 accessesView PDFCite