6 articles for “Second Order Initial Value Problems”

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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 accessEvery word in the titleThe Existence, Uniqueness and Error Bounds of Approximation Splines Interpolation for Solving Second-Order Initial Value ProblemsAbbas Y. Al Bayati, Rostam K. Saeed, Faraidun K. Hama-SalhProblem statement: The lacunary interpolation problem, which we had investigated in this study, consisted in finding the six degree spline S(x) of deficiency four, interpolating data given on the function value and third and fifth order in the interval [0,1]. Also, an extra initial condition was prescribed on the first derivative. Other purpose of this construction was to solve the … …Journal of Mathematics and Statistics, Vol. 5, Issue 2 · 30 Jun 2009 · 8,172 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsMultistep Collocation Block Method for Direct Solution of Second Order Ordinary Differential EquationsJohn Olusola Kuboye, Zurni OmarIn this study, block method of order six for solving second order ordinary differential equations is developed. The method of interpolation of approximated power series and collocation of its second derivative is adopted in the derivation of the method. The developed method is applied in block form to produce approximate solution at five points simultaneously. The stability properties of the … …American Journal of Applied Sciences, Vol. 12, Issue 9 · 13 Oct 2015 · 6,565 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsBlock Methods based on Newton Interpolations for Solving Special Second Order Ordinary Differential Equations DirectlyYap Lee Ken, Fudziah Ismail, Mohamed Suleiman, Suriah Md. AminThis study focused mainly on the derivation of the 2 and 3-point block methods with constant coefficients for solving special second order ordinary differential equations directly based on Newton-Gregory backward interpolation formula. The performance of the new methods was compared with the conventional 1-point method using a standard set of test problems. Numerical results were presented to illustrate the effectiveness … …Journal of Mathematics and Statistics, Vol. 4, Issue 3 · 30 Sep 2008 · 8,120 accessesView PDF Cite

Research ArticleOpen accessIn the abstractA Non-Linear Absolutely-Stable Explicit Numerical Integration Algorithm for Stiff Initial-Value ProblemsEssam R. El-ZaharThe time-step in integration process has two restrictions. The first one is the time step restriction due to accuracy requirement τac and the second one is the time-step restriction due to stability requirement τst. The most of explicit methods have small stability regions and consequently small τst. It obliges us to solve stiff problems with small step size τst << … …American Journal of Applied Sciences, Vol. 10, Issue 11 · 11 Sep 2013 · 7,559 accessesView PDF Cite

Research ArticleOpen accessIn the abstractOn Sixtic Lacunary Spline Solutions of Second Order Initial Value ProblemJwamer Karwan Hama FarajProblem statement: The lacunary problem, which we had investigated in this study, consider in finding the spline function of degree six S(x) of deficiency four, interpolating data given on the function value and third, forth order in the interval [0,1]. Also, on the extra initial condition was prescribed on the first derivative. Other purpose of this construction was to solve … …Journal of Mathematics and Statistics, Vol. 5, Issue 4 · 31 Dec 2009 · 7,763 accessesView PDF Cite