Malik Suheel Abdullah, Qureshi Ijaz Mansoor, Amir Muhammad, Haq Ihsanul
Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad, Pakistan.
Department of Electrical Engineering, Air University, Islamabad, Pakistan.
ScientificWorldJournal. 2014 Feb 2;2014:837021. doi: 10.1155/2014/837021. eCollection 2014.
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.
我们提出了一种混合启发式计算方法，用于求解生理学中出现的非线性奇异边值问题的数值解。近似解被推导为一些对数Sigmoid基函数的线性组合。构建了一个适应度函数，它表示给定非线性常微分方程（ODE）及其边界条件的均方误差之和。通过基于遗传算法（GA）、内点算法（IPA）和活动集算法（ASA）的混合启发式计算算法，对适应度函数中包含的未知可调参数进行优化。通过求解生理学中的三个例子，验证了所提方法的有效性和可行性。发现所得到的近似解与精确解以及一些传统数值解非常吻合。
