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401 articles for “Equations”
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Research ArticleOpen accessEvery word in the titleCost Analysis of A System with Preventive Maintenance by Using the Kolmogorov’s Forward Equations MethodKhaled Moh. El-SaidThis study deals with cost analysis of a two- unit cold standby redundant system with preventive maintenance.The random failure occurs at random times which follow an exponential distribution and also the repair time are assumed to be exponentially distributed. Using the Kolmogorov’s forward equations method. Several reliability characteristics are obtained. The mean time to system failure (MTSF) and the profit … …American Journal of Applied Sciences, Vol. 5, Issue 4 · 30 Apr 2008 · 7,067 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleMaximum Principles for Second Order Elliptic Equations in Nondivergence Form and ApplicationsMohammad Al-MahameedThe main objectives of this study were to introduce a maximum principle for second order elliptic equations in nondivergence form and to use a nondivergence technique called the ABP method to establish the maximum principles in small domains. The advantage of this work was that we obtain a maximum principle for equations with discontinuous coefficients of the leading terms and … …Journal of Mathematics and Statistics, Vol. 4, Issue 1 · 31 Mar 2008 · 6,859 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleA New Approach to Solve Nonlinear Partial Differential EquationsAbdoul R. Ghotbi, M. A. Mohammadzade, A. Avaei, M. KeyvanipoorNonlinear phenomena play a crucial role in applied mathematics and physics. Explicit solutions to the nonlinear equations are of fundamental importance. Various methods for obtaining explicit solution to nonlinear evolution equations have been proposed. In this letter homotopy perturbation method (HPM) is employed for solving one-dimensional non-homogeneous parabolic partial differential equation with a variable coefficient and a system of nonlinear … …Journal of Mathematics and Statistics, Vol. 3, Issue 4 · 31 Dec 2007 · 6,919 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleApproximate Analytical Solutions For Time-Dependent Emden-Fowler-Type Equations By Variational Iteration MethodKhaled BatihaThe main objective of the current study was to solve the time-dependent Emden-Fowler-type equation with singular behavior. The technique used here was called the variational iteration method (VIM). The advantage of this work is twofold. Firstly, the VIM reduces the computational work. Secondly, in comparison with existing techniques, the VIM is an improvement with regard to its accuracy and rapid … …American Journal of Applied Sciences, Vol. 4, Issue 7 · 31 Jul 2007 · 6,594 accessesView PDFCite
Research ArticleOpen accessEvery word 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 · 6,826 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleA Generalization of the Frobenius Method for Ordinary Differential Equations with Regular Singular PointsJung-Hua Chou, Raylin WuThe conventional Frobenius method for second order differential equations with regular singular points is extended to differential equations of higher and lower orders. The conditions of a point being regular singular are addressed. It is also shown that Cauchy-Euler differential equations are a special case of ordinary differential equations with regular singular points. …Journal of Mathematics and Statistics, Vol. 1, Issue 1 · 31 Mar 2005 · 7,545 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleThe Solution to Some Hypersingular Integral EquationsAlexander G. RammGel’fand, I. M., & Shilov, G. E. (1964). Generalized Functions. Volume I: Properties and Operations (1st ed., Vol. 1). Academic Press. Hörmander, L. (1998). The Analysis of Linear Partial Differential Operators I (1st ed.). Springer Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96750-4 Ramm, A. G. (2022). The Navier-Stokes Problem (2nd ed.). Springer Nature. Ramm, A. G. (2023). Analysis of the Navier-Stokes problem (2nd ed.). … …Journal of Mathematics and Statistics, Vol. 20, Issue 1 · 25 May 2024 · 5,686 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleNonlinear Piecewise-Defined Difference Equations with Reciprocal Quadratic TermsRamadan Sabra, Saleem Shafiq Al-AshhabIn this study we consider the several types of piece-wise defined sequences. We prove some results concerning the behavior of the sequence. In some cases we prove that the terms repeat themselves in certain patterns and we prove in other cases that the terms grow monotonically after few terms and approaches infinity. …Journal of Mathematics and Statistics, Vol. 11, Issue 3 · 18 Nov 2015 · 6,767 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleUncertainty Analysis of Time of Concentration Equations based on First-Order-Analysis (FOA) MethodAsghar AzizianThe time of concentration (Tc) is one the most important time parameters to predict the response of a catchment to a given rainfall and plays a key role in the hydrologic design and rainfall-runoff modeling. There are a huge number of empirical/semi-empirical equations for estimation of Tc and depending on several parameters such as rainfall attributes, topographic and land cover … …American Journal of Engineering and Applied Sciences, Vol. 11, Issue 1 · 19 Mar 2018 · 9,303 accessesView PDFCite