Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in PhysiologyReport as inadecuate




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The Scientific World Journal - Volume 2014 2014, Article ID 837021, 10 pages -

Research Article

Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad, Pakistan

Department of Electrical Engineering, Air University, Islamabad, Pakistan

Received 31 August 2013; Accepted 18 November 2013; Published 2 February 2014

Academic Editors: L. Guerrini and J. Pérez

Copyright © 2014 Suheel Abdullah Malik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm GA, interior point algorithm IPA, and active set algorithm ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.





Author: Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Amir, and Ihsanul Haq

Source: https://www.hindawi.com/



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