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155 articles for “Differential Equation”
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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 titleAn Improved Positivity Preserving Odd Degree-N Said-Ball Boundary Curves on Rectangular Grid Using Partial Differential EquationAhmed Kherd, Azizan Saaban, Noraziah Haji ManThis paper discusses the sufficient conditions for positivity preserving odd degree-n Said-Ball boundary curves defined on a rectangular grid. We derive a sufficient condition on boundary curves of rectangular Said-Ball patches where the lower bound ordinates are adjusted independently. To construct the boundary curves for each rectangular patch, the Said-Ball polynomial solution of fourth order PDE will be considered where … …Journal of Mathematics and Statistics, Vol. 12, Issue 1 · 10 Apr 2016 · 6,740 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleExistence Results for a Class of Nonlinear Hadamard Fractional with p-Laplacian Operator Differential EquationsSamah HorrigueIn this study, we are concerned with the existence and uniqueness of solution for some nonlinear Hadamard fractional differential equations. Our results are based on different classical fixed point theorems. Some useful examples are presented in order to illustrate the validity of our main results. …Journal of Mathematics and Statistics, Vol. 17, Issue 1 · 2 Oct 2021 · 6,886 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 titleOn Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS DiseaseS. A.A. El-MaroufProblem statement: This study aims to discuss the stability and bifurcation of a system of ordinary differential equations expressing a general nonlinear model of HIV/AIDS which has great interests from scientists and researchers on mathematics, biology, medicine and education. The existance of equilibrium points and their local stability are studied for HIV/AIDS model with two forms of the incidence rates. … …American Journal of Applied Sciences, Vol. 9, Issue 7 · 24 Apr 2012 · 7,018 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 Zero-Stable Optimal Order Method for Direct Solution of Second Order Differential EquationsKayode Sunday JacobProblem statement: In this study, a numerical method for direct solution of general second order differential equations was considered in order to circumvent the problems of computational burden and computer time wastage associated with method of reduction to system of first order equations. The issue of zero stability of higher order methods is considered in the development of the method. … …Journal of Mathematics and Statistics, Vol. 6, Issue 3 · 30 Sep 2010 · 7,068 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleNumerical Solution of Second-Order Linear Fredholm Integro-Differential Equation Using Generalized Minimal Residual MethodElayaraja Aruchunan, Jumat SulaimanProblem statement: This research purposely brought up to solve complicated equations such as partial differential equations, integral equations, Integro-Differential Equations (IDE), stochastic equations and others. Many physical phenomena contain mathematical formulations such integro-differential equations which are arise in fluid dynamics, biological models and chemical kinetics. In fact, several formulations and numerical solutions of the linear Fredholm integro-differential equation of second … …American Journal of Applied Sciences, Vol. 7, Issue 6 · 30 Jun 2010 · 8,198 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 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