Operational matrix method for solving Riccati differential equation by using hybrid third kind Chebyshev polynomials and block-pulse functions

Abstract

The present operational matrix method reduces the Riccati differential equation to a system of algebraic equations. The algebraic system has been solved numerically by Tau method. Convergence analysis of the present method has been discussed in this article. Meanwhile, a numerical method is presented for solving Riccati differential equation. There has also been introduced the operational matrices of derivative and product based on hybrid third kind Chebyshev polynomials and block-pulse functions. Moreover, numerical examples have been included to demonstrate the validity and applicability of the technique.