درمان عددی برای مشکلات مرزی معادلات دیفرانسیل تابع پانتو گراف با استفاده از الگوریتم های هوشمند محاسباتی

In this study, stochastic computational techniques are developed for the solution of boundary value problems (BVPs) of second order Pantograph functional differential equation (PFDE) using artificial neural networks(ANNs), simulated annealing (SA), pattern search (PS), genetic algorithms (GAs), active-set algorithm (ASA) and their hybrid combinations. The strength of ANNs is exploited to construct a model for PFDE by defining as unsupervised error to approximate the solution. The accuracy of the model is subjected to find the appropriate design parameters of the networks. These optimal weights of the networks are trained using SA, PS and GAs, used as a tool for viable global search, hybridized with ASA for rapid local convergence. The designed schemes are evaluated by solving a numbers of BVPs for the PFDE and comparing with standard results. The reliability and effectiveness of the proposed solvers are investigated through Monte-Carlo simulations and their statistical analysis.