Title: Operational matrix method for solving Riccati differential equation by using hybrid third kind Chebyshev polynomials and block-pulse functions
Authors: Reza Jafari
Addresses: Department of Mathematics, Islamic Azad University, Miandoab Branch, Miandoab, Iran
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.
Keywords: hybrid functions; Chebyshev polynomials; block-pulse functions; operational matrix of derivative; Riccati differential equation.
International Journal of Mathematics in Operational Research, 2021 Vol.19 No.2, pp.161 - 179
Received: 03 Nov 2019
Accepted: 20 Feb 2020
Published online: 20 Jul 2021 *