Search results for: Chinwendu. B. Eleje

3 Approximated Solutions of Two-Point Nonlinear Boundary Problem by a Combination of Taylor Series Expansion and Newton Raphson Method

Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor

Abstract:

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.

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2 An Insurer’s Investment Model with Reinsurance Strategy under the Modified Constant Elasticity of Variance Process

Authors: K. N. C. Njoku, Chinwendu Best Eleje, Christian Chukwuemeka Nwandu

Abstract:

One of the problems facing most insurance companies is how best the burden of paying claims to its policy holders can be managed whenever need arises. Hence there is need for the insurer to buy a reinsurance contract in order to reduce risk which will enable the insurer to share the financial burden with the reinsurer. In this paper, the insurer’s and reinsurer’s strategy is investigated under the modified constant elasticity of variance (M-CEV) process and proportional administrative charges. The insurer considered investment in one risky asset and one risk free asset where the risky asset is modeled based on the M-CEV process which is an extension of constant elasticity of variance (CEV) process. Next, a nonlinear partial differential equation in the form of Hamilton Jacobi Bellman equation is obtained by dynamic programming approach. Using power transformation technique and variable change, the explicit solutions of the optimal investment strategy and optimal reinsurance strategy are obtained. Finally, some numerical simulations of some sensitive parameters were obtained and discussed in details where we observed that the modification factor only affects the optimal investment strategy and not the reinsurance strategy for an insurer with exponential utility function.

Keywords: Reinsurance strategy, Hamilton Jacobi Bellman equation, power transformation, M-CEV process, exponential utility.

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1 The Role of Fluid Catalytic Cracking in Process Optimisation for Petroleum Refineries

Authors: Chinwendu R. Nnabalu, Gioia Falcone, Imma Bortone

Abstract:

Petroleum refining is a chemical process in which the raw material (crude oil) is converted to finished commercial products for end users. The fluid catalytic cracking (FCC) unit is a key asset in refineries, requiring optimised processes in the context of engineering design. Following the first stage of separation of crude oil in a distillation tower, an additional 40 per cent quantity is attainable in the gasoline pool with further conversion of the downgraded product of crude oil (residue from the distillation tower) using a catalyst in the FCC process. Effective removal of sulphur oxides, nitrogen oxides, carbon and heavy metals from FCC gasoline requires greater separation efficiency and involves an enormous environmental significance. The FCC unit is primarily a reactor and regeneration system which employs cyclone systems for separation. Catalyst losses in FCC cyclones lead to high particulate matter emission on the regenerator side and fines carryover into the product on the reactor side. This paper aims at demonstrating the importance of FCC unit design criteria in terms of technical performance and compliance with environmental legislation. A systematic review of state-of-the-art FCC technology was carried out, identifying its key technical challenges and sources of emissions. Case studies of petroleum refineries in Nigeria were assessed against selected global case studies. The review highlights the need for further modelling investigations to help improve FCC design to more effectively meet product specification requirements while complying with stricter environmental legislation.

Keywords: Design, emissions, fluid catalytic cracking, petroleum refineries.

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