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37 articles for “Ordinary Differential Equations”
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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 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 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 titleConvergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix CoefficientsO. Olotu, S.A. OlorunsolaThe geometric convergence ratio, the main focus of a discretized scheme for constrained quadratic control problem was examined. In order to allow for the numerical applications of the developed scheme, discretizing the time interval and using Euler’s scheme for its differential constraint obtained a finite dimensional approximation. Applying the penalty function method, an unconstrained problem was obtained on function minimization … …American Journal of Applied Sciences, Vol. 5, Issue 2 · 28 Feb 2008 · 7,108 accessesView PDFCite
Research ArticleOpen accessIn the keywordsComputational Analysis of Network ODE Systems in Metric Spaces: An ApproachSusmit BagchiTraditionally, the concepts of graph theory are applied to design stationary computer networks and, to analyze dynamics of social networks. However, the majority of non-stationary network models are formulated by using Ordinary Differential Equations (ODE) with varying orders having homogeneous or non-homogeneous forms. However, the analysis of continuous solution spaces of ODE and understanding of the interplay of spaces in … …Journal of Computer Science, Vol. 13, Issue 1 · 1 Mar 2017 · 7,891 accessesView PDFCite
Research ArticleOpen accessIn the keywordsTime-Delay Estimation using the Characteristic Roots of Delay Differential EquationsSun Yi, Wonchang Choi, Taher Abu-LebdehProblem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in formulation caused. Approach: The presented method makes use … …American Journal of Applied Sciences, Vol. 9, Issue 6 · 7 Apr 2012 · 8,082 accessesView PDFCite
Research ArticleOpen accessIn the keywordsSolving Directly Two Point Non Linear Boundary Value Problems Using Direct Adams Moulton MethodZanariah Abdul Majid, Phang Pei See, Mohamed SuleimanProblem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs) directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs). This approach is very well established but it obviously will enlarge the systems of … …Journal of Mathematics and Statistics, Vol. 7, Issue 2 · 18 May 2011 · 7,882 accessesView PDFCite
Research ArticleOpen accessIn the keywordsA New Perturbative Approach in Nonlinear Singularity AnalysisTat-Leung YeeProblem statement: The study is devoted to the “mirror” method which enables one to study the integrability of nonlinear differential equations. Approach: A perturbative extension of the mirror method is introduced. Results: The mirror system and its first perturbation are then utilized to gain insights into certain nonlinear equations possessing negative Fuchs indices, which were poorly understood in the literatures. … …Journal of Mathematics and Statistics, Vol. 7, Issue 3 · 29 Jul 2011 · 7,331 accessesView PDFCite