CLC number: TP183; O175
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2017-03-14
Cited: 1
Clicked: 6811
Muhammad Asif Zahoor Raja, Iftikhar Ahmad, Imtiaz Khan, Muhammed Ibrahem Syam, Abdul Majid Wazwaz. Neuro-heuristic computational intelligence for solving nonlinear pantograph systems[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(4): 464-484.
@article{title="Neuro-heuristic computational intelligence for solving nonlinear pantograph systems",
author="Muhammad Asif Zahoor Raja, Iftikhar Ahmad, Imtiaz Khan, Muhammed Ibrahem Syam, Abdul Majid Wazwaz",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="18",
number="4",
pages="464-484",
year="2017",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1500393"
}
%0 Journal Article
%T Neuro-heuristic computational intelligence for solving nonlinear pantograph systems
%A Muhammad Asif Zahoor Raja
%A Iftikhar Ahmad
%A Imtiaz Khan
%A Muhammed Ibrahem Syam
%A Abdul Majid Wazwaz
%J Frontiers of Information Technology & Electronic Engineering
%V 18
%N 4
%P 464-484
%@ 2095-9184
%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1500393
TY - JOUR
T1 - Neuro-heuristic computational intelligence for solving nonlinear pantograph systems
A1 - Muhammad Asif Zahoor Raja
A1 - Iftikhar Ahmad
A1 - Imtiaz Khan
A1 - Muhammed Ibrahem Syam
A1 - Abdul Majid Wazwaz
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 18
IS - 4
SP - 464
EP - 484
%@ 2095-9184
Y1 - 2017
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1500393
Abstract: We present a neuro-heuristic computing platform for finding the solution for initial value problems (IVPs) of nonlinear pantograph systems based on functional differential equations (P-FDEs) of different orders. In this scheme, the strengths of feed-forward artificial neural networks (ANNs), the evolutionary computing technique mainly based on genetic algorithms (GAs), and the interior-point technique (IPT) are exploited. Two types of mathematical models of the systems are constructed with the help of ANNs by defining an unsupervised error with and without exactly satisfying the initial conditions. The design parameters of ANN models are optimized with a hybrid approach GA–IPT, where GA is used as a tool for effective global search, and IPT is incorporated for rapid local convergence. The proposed scheme is tested on three different types of IVPs of P-FDE with orders 1–3. The correctness of the scheme is established by comparison with the existing exact solutions. The accuracy and convergence of the proposed scheme are further validated through a large number of numerical experiments by taking different numbers of neurons in ANN models.
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