Abstract: A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.
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.