Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method

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. Keywords—Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.