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37 articles for “ordinary differential equations”
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Research ArticleOpen accessPhrase in the titleExplicit 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 PDFCite
Research ArticleOpen accessPhrase in the titleAn Embedded Explicit Hybrid Method for Ordinary Differential EquationsF. Samat, F. IsmailProblem statement: Many differential systems that appear in practice were special second-order ordinary differential equations of the form y" = f (x, y). In the past research, there was a continuous need for methods for numerically solving these equations. Approach: This study describes the derivation and implementation of a pair of embedded explicit hybrid methods for solving non-stiff second-order ordinary … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 23 Dec 2011 · 7,417 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleBlock 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 PDFCite
Research ArticleOpen accessPhrase 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 · 7,540 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleOn the Pseudo-Spectral Method of Solving Linear Ordinary Differential EquationsB. S. OgundareProblem statement: Not all differential equations can be solved analytically, to overcome this problem, there is need to search for an accurate approximate solution. Approach: The objective of this study was to find an accurate approximation technique (scheme) for solving linear differential equations. By exploiting the Trigonometric identity property of the Chebyshev polynomial, we developed a numerical scheme referred to … …Journal of Mathematics and Statistics, Vol. 5, Issue 2 · 30 Jun 2009 · 7,222 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleNew Hybrid Block Method with Three Off-Step Points for Solving First Order Ordinary Differential EquationsRa’ft Abdelrahim, Zurni Omar, John Olusola KuboyeA new single-step hybrid block method with three off-step points for the solution of first order ordinary differential equations is proposed. The strategy employed to develop this method is interpolating the power series approximate solution at xn and off-step points and collocating the derivative of the power at xn+1. The class of linear multistep method derived is then simultaneously applied … …American Journal of Applied Sciences, Vol. 13, Issue 2 · 18 Feb 2016 · 8,234 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleMultistep 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 PDFCite
Research ArticleOpen accessPhrase in the titleNumerical Solution of Higher Order Ordinary Differential Equations by Direct Block CodeN. Waeleh, Z. A. Majid, F. Ismail, M. SuleimanProblem statement: This study is concerned with the development of a code based on 2-point block method for solving higher order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) directly. Approach: The block method was developed based on numerical integration and using interpolation approach which is similarly as Adams Moulton type. Furthermore, the proposed method is derived in order … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 3 Feb 2012 · 8,138 accessesView PDFCite
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 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