Operational matrices to solve nonlinear Riccati differential equations of an arbitrary order

In this paper, an effective numerical method to achieve the numerical solution of nonlinear Riccati differential equations of an arbitrary (integer and fractional) order has been developed. For this purpose, the fractional order of the Chebyshev functions (FCFs) based on the classical Chebyshev polynomials of the first kind have been introduced, that can be used to obtain the solution of these equations. Also, the operational matrices of fractional derivative and product for the FCFs have been constructed. The obtained results illustrated demonstrate that the suggested approaches are applicable and valid. Key words: fractional order of the Chebyshev functions; operational matrix; Riccati differential equations; Galerkin method; differential equation of arbitrary order.

Citation: K. Parand, M. Delkhosh, Operational matrices to solve nonlinear Riccati differential equations of an arbitrary order, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 100–115. DOI: 10.18721/JPM.10310