A new stochastic approach for solution of Riccati differential equation of fractional order

被引：77
|
作者：
Raja, Muhammad Asif Zahoor [1 ]
Khan, Junaid Ali [1 ]
Qureshi, Ijaz Mansoor [2 ]
机构：
[1] Int Islamic Univ, Dept Elect Engn, Fac Engn & Technol, Islamabad, Pakistan
[2] Air Univ, Dept Elect Engn, Islamabad, Pakistan
来源：
ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE | 2010年 / 60卷 / 3-4期
关键词：
Riccati equation; Non linear ODE; Fractional differential equation; Neural network; Swarm intelligence; Particle swarm optimization; Simulating annealing; HOMOTOPY PERTURBATION METHOD; NEURAL-NETWORKS; DECOMPOSITION;
D O I：
10.1007/s10472-010-9222-x
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this article, a stochastic technique has been developed for the solution of nonlinear Riccati differential equation of fractional order. Feed-forward artificial neural network is employed for accurate mathematical modeling and learning of its weights is made with heuristic computational algorithm based on swarm intelligence. In this scheme, particle swarm optimization is used as a tool for the rapid global search method, and simulating annealing for efficient local search. The scheme is equally capable of solving the integer order or fractional order Riccati differential equations. Comparison of results was made with standard approximate analytic, as well as, stochastic numerical solvers and exact solutions.
引用
收藏
页码：229 / 250
页数：22
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