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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 · 7,545 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 · 6,744 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 · 6,892 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 · 6,569 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 · 8,202 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 · 8,931 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 · 7,711 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleOn the Stability and Ultimate Boundedness of Solutions for Certain Third Order Differential EquationsA.T. Ademola, P.O. ArawomoProblem Statement: With respect to our observation in the relevant literature, work on stability and boundedness of solution for certain third order nonlinear differential equations where the nonlinear and the forcing terms depend on certain variables are scare. The objective of this study was to get criteria for stability and boundedness of solutions for these classes of differential equations. Approach: … …Journal of Mathematics and Statistics, Vol. 4, Issue 4 · 31 Dec 2008 · 6,915 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 · 7,177 accessesView PDFCite
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 · 7,506 accessesView PDFCite