Search results for: C. E. Abhulimen

3 A Class of Third Derivative Four-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations

Authors: Cletus Abhulimen, L. A. Ukpebor

Abstract:

In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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2 A Family of Second Derivative Methods for Numerical Integration of Stiff Initial Value Problems in Ordinary Differential Equations

Authors: Luke Ukpebor, C. E. Abhulimen

Abstract:

Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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1 Investigating the Performance of Power Industry in a Developing Nation for Industrialization and Environmental Security

Authors: Abel Edeowede Abhulimen

Abstract:

Due to supply irregularity and frequent outages, the need for reliability in power supply has grown unsatisfactorily over time in developing nations, impeding industrialization and fueling insecurity. This article attempts to break down the Nigerian power issue into its numerous sub-sectors in order to pinpoint the industry's ailment and suggest a viable fix. Monthly average performance data were obtained for the various sub-sectors across the industry for eight consecutive quarters. Whereas the amount of energy generated was found to be insufficient to engender industrialization in a nation like Nigeria, the transmission infrastructure was inadequate for the amount of power needed to be wheeled. Additionally, the distribution sub-sector was plagued with problems such as revenue collection inefficiency, severe enough to impede the growth of the entire industry. The country's goal of attaining energy sufficiency and industrialization would significantly be closer to reality with a conscious effort to increase the base of power generation through aggressive investment in Combined Cycle Gas Turbines (CCGT), decentralization of the transmission infrastructure, and strict monitoring of the distribution sub-sector for improved accountability and system reliability.

Keywords: performance, power industry, industrialization, security, energy

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