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120 articles for “Differential Equations”
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Research ArticleOpen accessPhrase in the titleA Multiderivative Collocation Method for 5th Order Ordinary Differential EquationsS. J. Kayode, D. O. AwoyemiProblem statement: The conventional methods of solving higher order differential equations have been by reducing them to systems of first order equations. This approach is cumbersome and increases computational time. Approach: To address this problem, a numerical algorithm for direct solution of 5th order initial value problems in ordinary differential equations (odes), using power series as basis function, is proposed … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 8,928 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleExterior Differential Systems for Higher Order Partial Differential EquationsPaul BrackenThe theory of exterior differential systems is applied to study integrability of a set of related partial differential equations expressed in the terms of differential forms using Cartan's method. The Camassa-Holm equation and the Degasperis-Procesi equations are special cases that are described by these exterior differential systems. Some conservation laws are obtained in the cases of the more relevant equations. … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 6,924 accessesView PDFCite
Research ArticleOpen accessPhrase 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 accessPhrase in the titleA New Block Method for Special Third Order Ordinary Differential EquationsB. T. Olabode, Y. YusuphA linear multistep method for the direct solution of initial value problems of ordinary differential equations was presented in this article. Collocation approximation method was adopted in the derivation of the scheme and then the scheme was applied as simultaneous integrator to special third order initial value problem of ordinary differential equations. The new block method possessed the desirable feature … …Journal of Mathematics and Statistics, Vol. 5, Issue 3 · 30 Sep 2009 · 7,707 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleOn the Stability and Ultimate Boundedness of Solutions for Certain Third Order Differential EquationsA.T. Ademola, P.O. ArawomoProblem Statement: With respect to our observation in the relevant literature, work on stability and boundedness of solution for certain third order nonlinear differential equations where the nonlinear and the forcing terms depend on certain variables are scare. The objective of this study was to get criteria for stability and boundedness of solutions for these classes of differential equations. Approach: … …Journal of Mathematics and Statistics, Vol. 4, Issue 4 · 31 Dec 2008 · 6,911 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleAn Order Six Zero-Stable Method for Direct Solution of Fourth Order Ordinary Differential EquationsKayode Sunday JacobA zero-stable numerical method for direct solution of fourth order differential equations reduces the computational burden and computer time wastage involved in the method of reducing such equations to a system of first order equations. The method adopted is the collocation of the differential system and the interpolation of the approximate solution to the problem using the power series as … …American Journal of Applied Sciences, Vol. 5, Issue 11 · 30 Nov 2008 · 7,170 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleK-Step Rational Runge-Kutta Method for Solution of Stiff System of Ordinary Differential EquationsP.O. Babatola, R.A. Ademiluyi, E.A. AreoThis study described the development, analysis and implementation of K-step implicit rational Runge-Kutta schemes for solution of stiff system of ordinary differential equations. Its development adopted taylor and binomial series expansion techniques to generate its parameters. The analysis of its basic properties adopted dalhquist a-stability model test equation and the results showed that the scheme was a-stable, consistent and convergent. … …Journal of Mathematics and Statistics, Vol. 4, Issue 3 · 30 Sep 2008 · 7,502 accessesView PDFCite
Research ArticleOpen accessPhrase 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 accessPhrase in the titleOn Computing of Eigenvalues of Differential Equations Q = λP with Eigenparameter in Boundary ConditionsS. M. Al-HarbiProblem statement: Our purpose of this study is to use sinc methods to compute approximately the eigenval-ues of second-order operator pencil of the form Q-λP. Approach: Where Q is second order self adjoint differential operator and P is a first order and λ∈C is an eigenvalue parameter. Results: The eigenparameter appears in the boundary conditions linearly. Using computable error boundswe … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 29 Jan 2011 · 6,826 accessesView PDFCite