Numerical solution of fractional-order Riccati differential equation by differential quadrature method based on Chebyshev polynomials

Abstract

Abstract We apply the Chebyshev polynomial-based differential quadrature method to the solution of a fractional-order Riccati differential equation. The fractional derivative is described in the Caputo sense. We derive and utilize explicit expressions of weighting coefficients for approximation of fractional derivatives to reduce a Riccati differential equation to a system of algebraic equations. We present numerical examples to verify the efficiency and accuracy of the proposed method. The results reveal that the method is accurate and easy to implement.

Keywords

• Differential quadrature
• Riccati differential equation
• Chebyshev polynomial
• Caputo derivative