7 results for “Taylor series expansion”

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Research ArticleOpen accessPhrase in the titleHybrid Block Method for Direct Numerical Approximation of Second Order Initial Value Problems Using Taylor Series ExpansionsOluwaseun Adeyeye, Zurni OmarIn this article, a hybrid block method is utilized for the numerical approximation of second order Initial Value Problems (IVPs). The rigor of reduction to a system of first order initial value problems is bypassed as the hybrid block method directly solves the second order IVPs. Likewise, the methodology utilized also avoids the cumbersome steps involved in the widely adopted … …American Journal of Applied Sciences, Vol. 14, Issue 2 · 17 Feb 2017 · 7,953 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsNeural-Based Models of Semiconductor Devices for SPICE SimulatorHanene Ben Hammouda, Mongia Mhiri, Zièd Gafsi, Kamel BesbesThe paper addresses a simple and fast new approach to implement Artificial Neural Networks (ANN) models for the MOS transistor into SPICE. The proposed approach involves two steps, the modeling phase of the device by NN providing its input/output patterns, and the SPICE implementation process of the resulting model. Using the Taylor series expansion, a neural based small-signal model is … …American Journal of Applied Sciences, Vol. 5, Issue 4 · 30 Apr 2008 · 8,577 accessesView PDF Cite

Research ArticleOpen accessIn the abstractThe Magnetic Field Induced by a Lightning Strike's Indirect Effect Double Exponential Current WaveformScott L. Meredith, Susan K. Earles, Ivica N. Kostanic, Niescja E. TurnerProblem statement: Develop a new formula which describes the magnetic field induced by a lightning strike’s indirect effect double exponential current waveform. Approach: A novel approach for developing a closed-form solution for the magnetic field from the indirect effect double exponential current waveform will be presented. In the literature, models typically employ the pulse waveform to derive the corresponding electromagnetic … …Journal of Mathematics and Statistics, Vol. 6, Issue 3 · 30 Sep 2010 · 8,191 accessesView PDF Cite

Research ArticleOpen accessIn the abstractK-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 PDF Cite

Research ArticleOpen accessIn the abstractComputational Discrete Time Markov Chain with Correlated Transition ProbabilitiesPeerayuth CharnsethikulThis study presents a computational procedure for analyzing statistics of steady state probabilities in a discrete time Markov chain with correlations among their transition probabilities. The proposed model simply uses the first order Taylor’s series expansion and statistical expected value properties to obtain the resulting linear matrix equations system. Computationally, the bottleneck is O(n4) but can be improved by distributed … …Journal of Mathematics and Statistics, Vol. 2, Issue 4 · 31 Dec 2007 · 6,648 accessesView PDF Cite

Research ArticleOpen accessAll words, across the recordExplicit Direct Integrators of RK Type for Solving Special Fifth-Order Ordinary Differential EquationsMohammed S. Mechee, Murtaza A. KadhimThe main contribution of this paper is the development of direct explicit methods of Runge-Kutta (RK) type for solving special fifth-Order Ordinary Differential Equations (ODEs). For this purpose, we have generalized RKD and RKT methods of special third and fourth-order ODEs. Using Taylor expansion, we have derived the algebraic equations of algebraic equations of order conditions for the proposed RKM … …American Journal of Applied Sciences, Vol. 13, Issue 12 · 26 Dec 2016 · 7,940 accessesView PDF Cite

Research ArticleOpen accessAll words, across the recordAn Expansion Iterative Technique for Handling Fractional Differential Equations Using Fractional Power Series SchemeRadwan Abu-Gdairi, Mohammed Al-Smadi, Ghaleb GumahIn this study, we present a new analytical numerical technique for solving a class of time Fractional Differential Equations (FDEs) with variable coefficients based on the generalized Taylor series formula in the Caputo sense. This method provided the solution in the form of a rapidly convergent power series under a multiple fractional differentiability with easily computable components. An efficacious experiment … …Journal of Mathematics and Statistics, Vol. 11, Issue 2 · 18 Sep 2015 · 7,807 accessesView PDF Cite