International Journal Of Scientific & Engineering Research

 Journal

 A Predictor-Corrector Hybrid Method For Numerical Approximation Of Third-Order Initial Value Problems

 Obarhua, F. O.

 2022

For solving third order ordinary differential equations, this work discusses a numerical integrator with continuous coefficients. For the approximate solution of the differential equations, a combination of power series and exponential function has been employed as the basis function in the formulation of the integrators. To produce a system of linear equations, the approximation solution and the accompanying differential system were interpolated and collocated, respectively. The method developed is accurate to a high order, stable, and convergent, making it suited for the integration of stiff systems of initial value problems of odes. The idea of creating initial values with a lower order of accuracy than the main scheme was avoided in this study by providing the same order of accuracy as the main technique. The integration identities as equal areas under the various segments of the solution curves over the integration intervals brought to the natural retention of symmetry as a result of this novel idea. The application of this newly discovered multistep integration method to a number of well-known issues in the literature yields correct results at a cheap cost of computing. When compared to previous methods, the results appear to be more accurate. 

 International Journal Of Mathematics In Operation Research.

 Journal

 Algorithms Of Algebraic Order Nine For Numerically Solving Second-Order Boundary And Initial Value Problems In Ordinary Differential Equations

 (xiii) Omole, O.O., *Obarhua, F.O., Familua A.B., Shokri, A.

 2022

A new numerical algorithm comprising of two-step with six off-step points is presented in this paper. The new method adopted interpolation of the approximate solution and collocation of the differential system in the development of the methods. The main method and its supplementary methods are combined to form the required integrators which are self-starting in nature. The implementation strategy is discussed and the new method has an algebraic order nine with significant properties that vindicate its effectiveness when applied to solve some standard second-order initial and boundary problems of ordinary differential equations such as nonlinear problem, variable coefficient problem, stiff problem, two body problem, Classical nonlinear Bratu’s BVP in one-dimensional planar coordinates, Troesch’s problem, Michaelis-Menten oxygen diffusion problem with uptake kinetic and the van der Pol oscillatory problem. The comparison of the new methods with some already existing methods confirmed that the method gives better accuracy. The effectiveness and efficiency are also demonstrated in the curves. 

 Journal Of Nigerian Physical Sciences

 Journal

 An Order Four Continuous Numerical Method For Solving General Second Order Ordinary Differential Equations

 F.O. OBARHUA & J.O. KAYODE

 2021

Continuous hybrid methods are now recognized as efficient numerical methods for problems whose solutions have finite domains or cannot be solved analytically. In this work, the continuous hybrid numerical method for the solution of general second order initial value problems of ordinary differential equations is considered. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is zero stable, consistent, convergent. It is suitable for both non-stiff and mildly-stiff problems and results were found to compete favorably with the existing methods in terms of accuracy. 

 Asian Research Journal Of Mathematics

 Journal

 An Order Six Stormer-cowell-type Method For Solving Directly Higher Order Ordinary Differential Equations

 S. J. Kayode, O. S. Ige1*, F. O. Obarhua And E. O. Omole

 2018

This paper considers the development of an efficient Stormer-Cowell-Typed method for the direct solution of second order ordinary differential equations using the method of interpolation of the combination of Cheybeshev and Legendre polynomials approximate solution and collocation of the differential system to develop our scheme. The method derived was tested and confirmed to be consistent, stable within the region of absolute stability and zero-stable. The method was tested on some numerical examples and found to give a better approximation. 

 Journal Of The Nigerian Association Of Mathematical Physics

 Journal

 An Accurate Four-Point Hybrid Block Method For The Solution Of General Third Order Differential Equations

 Obarhua, F. O. And Kayode, S. J. And Areo E. A.

 2018

An accurate four-point hybrid block method for the solution of general third order initial value problem of ordinary differential equations is considered. In the development of the method, collocation and interpolation approaches are adopted using the combination of power series and exponential function approximate solution as the basis function. The developed order six method is applied to solve some third order ordinary differential equations for the purpose of comparison with existing methods of same order of accuracy. From the numerical results obtained, it is observed that the new hybrid block method is better than the previous numerical methods in literature in terms of accuracy. 

 Open Access Library Journal

 Journal

 An Eight Order Two-Step Taylor Series Algorithm For The Numerical Solutions Of Initial Value Problems Of Second Order Ordinary Differential Equations

 A. O. Owolanke*, O. Uwaheren, F. O. Obarhua

 2017

Our focus is the development and implementation of a new two-step hybrid method for the direct solution of general second order ordinary differential equation. Power series is adopted as the basis function in the development of the method and the arising differential system of equations is collocated at all grid and off-grid points. The resulting equation is interpolated at selected points. We then analyzed the resulting scheme for its basic properties. Numerical examples were taken to illustrate the efficiency of the method. The results obtained converge closely with the exact solutions. 

 International Journal Of Scientific & Engineering Research

 Journal

 SYMMETRIC 2-STEP 4-POINT HYBRID METHOD FOR THE SOLUTION OF GENERAL THIRD ORDER DIFFERENTIAL EQUATIONS

 S. J. Kayode And F.O. Obarhua*

 2017

This research considers a symmetric hybrid continuous linear multistep method for the solution of general third order ordinary differential equations. The method is generated by interpolation and collocation approach using a combination of power series and exponential function as basis function. The approximate basis function is interpolated at both grid and off-grid points but the collocation of the differential function is only at the grid points. The derived method was found to be symmetric, consistent, zero stable and of order six with low error constant. Accuracy of the method was confirmed by implementing the method on linear and non-linear test problems. The results show better performance over known existing methods solved with the same third order problems. 

 Open Access Library Journal

 Journal

 Symmetric Hybrid Linear Multistep Method For General Third Order Differential Equations

 Obarhua, F.O. And Kayode, S.J.

 2016

A symmetric hybrid linear multistep method for direct solution of general third order ordinary differential equations is considered in this paper. The method is developed by interpolation and collocation approach using a combination of power series and exponential function as basis function. The consistency, stability, order and error constant of the method were determined. The results showed that the method is consistent, zero stable and of order five with low error constant. The accuracy compared favorably over existing methods with higher order of accuracy. 

 Theoretical Mathematics & Applications

 Journal

 3-Step Hybrid Methods For Direct Numerical Integration Of Second Order IVPs Of ODEs.

 Kayode, S.J. And Obarhua, F.O.

 2015

The aim of this study is to produce consistent two-step y-function hybrid numerical methods for a direct solution of general second-order differ- ential equations. The basis function is interpolated at both grid and off-grid points and its associated differential system are collocated at all grid points. The method developed is This article is concerned with implicit y¡function hybrid numerical methods for direct integration solution of general second-order differential equations. The approach is based on interpolation of the basis function at both grid and off-grid points and collocation of its associated differential system at all grid points using power series as the basis function to the solution of the problem. The methods developed are continuous, consistent, and symmetric and the main predictor of the same order of accuracy with the methods was also developed to evaluate the implicit scheme. Comparisons of results of the derived methods with existing methods of higher order of accuracy show that the proposed method is better than the existing methods. 

 International Journal Of Advanced Scientific & Technical Research.ring Research

 Journal

 CONTINUOUS DOUBLE-HYBRID POINT METHOD FOR THE SOLUTION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

 Olanegan, O. O., Awoyemi, D. O., Ogunware, B. G. And Obarhua, F. O.

 2015

This research considers a continuous two-point hybrid for the general solution of second order ordinary differential equations with initial value problem (IVPs). The approximate solution is generated through power by the interpolation and collocation of the differential system. Taylor’s series approximation was used to analyse and implement. The method is found to be consistent and zero-stable. The numerical results show better efficiency and accuracy compared to existing method of other authors.