Remi Odekunle | Modibbo Adama University of Technology, Yola (original) (raw)

Papers by Remi Odekunle

American Journal of Computational and Applied Mathematics, 2016

Damping is an influence within or upon an oscillatory system that has the effect of reducing, res... more Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. A one-step sixth-order computational method is proposed in this paper for the solution of second order free undamped and free damped motions in mass-spring systems. The method of interpolation and collocation of power series approximate solution was adopted to generate a continuous computational hybrid linear multistep method which was evaluated at grid points to give a continuous block method. The resultant discrete block method was recovered when the continuous block method was evaluated at selected grid points. The basic properties of the method was also investigated and found to be zero-stable, consistent and convergent.

WSEAS TRANSACTIONS ON MATHEMATICS

This research study is aimed at developing variable step reduction block solver (VSRBS) for stiff... more This research study is aimed at developing variable step reduction block solver (VSRBS) for stiff ODEs. This step reduction block solver will embrace the technic of variable step-variable order to determine suited variable step size. The trigonometrically fitted method will represent the basis function approximation to be utilized together with the method of interpolation and collocation to derive (VSRBS). VSRBS comes with advantages to overcome the barrier of stability requirement pose by definition 4. Some selected modelled examples of stiff ODEs will solved and compared with existing methods to establish the efficiency and accuracy.

A method of collocation and interpolation of the power series approximate solution at some grid a... more A method of collocation and interpolation of the power series approximate solution at some grid and off-grid points is considered to generate a continuous linear multistep method for the solution of general second order initial value problems at constant step size. We use continuous block method to generate independent solutions which serves as predictors at selected points within the interval of integration. The efficiency of the proposed method was tested and was found to compete favorably with the existing methods.

Over the years, scientific computing has contributed immensely to computational mathematics. Math... more Over the years, scientific computing has contributed immensely to computational mathematics. Mathematica computer programming codes is known to provide computation and quick results. This research article is specifically built to generate Mathematica computer programming codes of exponentially fitted concurrent Milne’s device (EFCMD) for solving special problems. Exponentially fitted concurrent Miln device is formulated via collocation/interpolation with power series as the approximate solution. Analyzing the EFCMD will produce the main local truncation error (MLTE) after showing the order, results were shown to demonstrate the functioning of Mathematica programming codes of EFCMD for resolving special problems at some selected bounds of convergence. The finished results were obtained with the assistance of Mathematica 9 kernel. Numerical results display that EFCMD do better than existing methods in terms of the maximum errors in the least studied bound of convergence as a result of...

American Journal of Computational and Applied Mathematics, 2015

First order one-stage explicit Stochastic Rational Runge-Kutta methods were derived for the solut... more First order one-stage explicit Stochastic Rational Runge-Kutta methods were derived for the solution of stochastic ordinary differential equations. The derivation is based on the use of Taylor series expansion for both the deterministic and stochastic parts of the stochastic differential equation. The stability and convergence of the methods, found to be absolute stable. These methods were further tested on some numerical problems. From the results obtained, it is obvious that the derived methods; performed better than the ones with which we have analysed and they were compared with our results.

There exist large varieties of conjugate gradient algorithms. In order to take advantage of the a... more There exist large varieties of conjugate gradient algorithms. In order to take advantage of the attractive features of Liu and Storey (LS) and Conjugate Descent (CD) conjugate gradient methods, we suggest hybridization of these methods in which the parameter is computed as a convex combination of and respectively which the conjugate gradient (update) parameter was obtained from Secant equation. The algorithm generates descent direction and when the iterate jam, the direction satisfy sufficient descent condition. We report numerical results demonstrating the efficiency of our method. The hybrid computational scheme outperform or comparable with known conjugate gradient algorithms. We also show that our method converge globally using strong Wolfe condition.

Journal of the Nigerian Mathematical Society, 2020

This paper discusses the development of a new numerical solution of second order linear Fredholm ... more This paper discusses the development of a new numerical solution of second order linear Fredholm Volterra integro-dffierential equations by Legendre collocation method. The Fredholm Volterra integro-differential equation is rst converted into integral equation and then transformed into linear algebraic equations which are then solved using matrix inversion method. Numerical solution shows that the method gives better accuracy than the existing methods.

2014 IEEE 6th International Conference on Adaptive Science & Technology (ICAST), 2014

Several studies have shown that the power consumption of Information and Communications Technolog... more Several studies have shown that the power consumption of Information and Communications Technology (ICT) nodes account for up to 3% of the worldwide power supply and that they are responsible for 2% of the global carbon dioxide (C02) emission. However, several initiatives are being put in place to reduce the power consumption of the ICT sector in general. To this goal, we propose a novel model. The new model, which is developed based upon input-oriented Chanes, Cooper and Rhodes (CCR) data envelopment analysis (DEA) methodology is an alternative solution to the existing minimum power multicast methodology that is developed using Multicast Incremental Power (MD?) algorithm. The simulation result of the MD? algorithm is compared with the empirical DEA model, and the results, using DEA implementation, show that it is possible to further reduce the average multicast power in Wireless Sensor Networks (WSNs) if they operate efficiently.

American Journal of Computational Mathematics, 2013

2013 Fifth International Conference on Computational Intelligence, Communication Systems and Networks, 2013

ABSTRACT Next Generation Network (NGN) services and applications such as Digital Multimedia Broad... more ABSTRACT Next Generation Network (NGN) services and applications such as Digital Multimedia Broadcasting (DMB) and Internet Protocol Television (IPTV) will offer multicast features, but due to high traffic volume and high number of receivers there will be challenges of efficient multicast mechanisms for communication. With the rapid development of applications and networks, there is a need to optimize the transmission energy within a multicast group for efficient traffic in both wired and wireless channels. This paper discusses major algorithms for multicasting and then focuses on the analysis of Multicast Incremental Power (MIP) algorithm and the recently proposed Network coding based (NC) algorithm using energy-efficiency as metric. The performance of these algorithms are evaluated and optimized for energy reduction on communication networks. The results show a reduction in multicast energy as network size increases with decrease in multicast energy as the multicast group size increases for both wired and wireless networks.

Global Journal of Mathematical Sciences, 2010

The transcendental character of the polynomial equation of the retarded differential system makes... more The transcendental character of the polynomial equation of the retarded differential system makes it difficult to express its solution explicitly. This has cause a set back in the asymptotic stability analysis of the system solutions. Various acceptable mathematical techniques have been used to address the issue. In this paper, the integral-differential equation and the positive symmetric properties of given matrices are used in formulating a Lyapunov functional. The introduction of convex set segment of a symmetric matrix is explored to establish boundedness of the first derivative of the formulated functional. The integral-differential equation is utilized in computing the maximum delay interval for the system to attain stability. Its application to numerical problems confirms the suitability of the test.

Applied Mathematics, 2014

Theory has it that increasing the step length improves the accuracy of a method. In order to affi... more Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power series approximate solution at some selected grid points is considered so as to generate continuous linear multistep methods with constant step sizes. Two, three and four interpolation points are considered to generate the continuous predictor-corrector methods which are implemented in block method respectively. The proposed methods when tested on some numerical examples performed more efficiently than those of [1]. Interestingly the concept of self starting [2] and that of constant order are reaffirmed in our new methods.

This paper examines the development of one step, five hybrid point method for the solution of fir... more This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Journal of Mathematical and Computational Science, Jul 7, 2015

In this paper, we develop a block method using Chebyshev polynomial basis function and use it to ... more In this paper, we develop a block method using Chebyshev polynomial basis function and use it to produce discrete methods which are simultaneously applied as numerical integrators by assembling them into a block method. The paper further investigates the properties of the block method and found it to be zero-stable, consistent and convergent. We also tested the efficiency of the method on some sampled oscillatory problems and found out that the method performed better than some existing ones with which we compared our results.

In this paper, we consider the development of an extended block integrator for the solution of st... more In this paper, we consider the development of an extended block integrator for the solution of stiff and oscillatory first-order Ordinary Differential Equations (ODEs) using interpolation and collocation techniques. The integrator was developed by collocation and interpolation of the combination of power series and exponential function to generate a continuous implicit Linear Multistep Method (LMM). The paper further investigates the basic properties of the block integrator and found it to be zero-stable, consistent and convergent. The integrator was also tested on some sampled stiff and oscillatory problems and found to perform better than some existing ones.

For any numerical integrator to be efficient, ingenious and computationally reliable, it is expec... more For any numerical integrator to be efficient, ingenious and computationally reliable, it is expected that it be convergent, consistent and stable. In this paper, we develop a new numerical integrator which is particularly well suited for solving initial value problems in ordinary differential equations. The algorithm developed is based on a local representation of the theoretical solution to the initial value problem by a nonlinear interpolating function (comprising of the combination of polynomial, exponential and cyclometric functions). We further test whether or not the integrator satisfies the conditions for convergence, consistence and stability. From the analysis presented, it is obvious that the new numerical integrator can provide accurate solution to the original differential equation.

International Journal of Mathematics and Soft Computing

International Journal of Industrial Optimization

One of todays’ best-performing CG methods is Dai-Liao (DL) method which depends on non-negative p... more One of todays’ best-performing CG methods is Dai-Liao (DL) method which depends on non-negative parameter and conjugacy conditions for its computation. Although numerous optimal selections for the parameter were suggested, the best choice of remains a subject of consideration. The pure conjugacy condition adopts an exact line search for numerical experiments and convergence analysis. Though, a practical mathematical experiment implies using an inexact line search to find the step size. To avoid such drawbacks, Dai and Liao substituted the earlier conjugacy condition with an extended conjugacy condition. Therefore, this paper suggests a new hybrid CG that combines the strength of Liu and Storey and Conjugate Descent CG methods by retaining a choice of Dai-Liao parameterthat is optimal. The theoretical analysis indicated that the search direction of the new CG scheme is descent and satisfies sufficient descent condition when the iterates jam under strong Wolfe line search. The algor...

This research paper examines the derivation and implementation of a new 4-point block method for ... more This research paper examines the derivation and implementation of a new 4-point block method for direct integration of first-order ordinary differential equations using interpolation and collocation techniques. The approximate solution is a combination of power series and exponential function. The paper further investigates the properties of the new integrator and found it to be zero-stable, consistent and convergent. The new integrator was tested on some numerical examples and found to perform better than some existing ones.

Applied Mathematics and Computation, 2004

A class of methods for the numerical solution of initial value problems whose solution has singul... more A class of methods for the numerical solution of initial value problems whose solution has singular point(s) shall be discussed. They are A-and L-stable and were found to perform efficiently well when faced with singularity problem but perform poorly when applied to non-singular problems.