Abstract: An evolutionary computing technique for solving initial value problems in Ordinary Differential Equations is proposed in this paper. Neural network is used as a universal approximator while the adaptive parameters of neural networks are optimized by genetic algorithm. The solution is achieved on the continuous grid of time instead of discrete as in other numerical techniques. The comparison is carried out with classical numerical techniques and the solution is found with a uniform accuracy of MSE ≈ 10-9 .
Abstract: In this article an evolutionary technique has been used
for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for
the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been
successfully applied to solve the different forms of Riccati
differential equations. The strength of proposed method has in its
equal applicability for the integer order case, as well as, fractional
order case. Comparison of the method has been made with standard
numerical techniques as well as the analytic solutions. It is found
that the designed method can provide the solution to the equation
with better accuracy than its counterpart deterministic approaches.
Another advantage of the given approach is to provide results on
entire finite continuous domain unlike other numerical methods
which provide solutions only on discrete grid of points.