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

[摘要] 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.

[学科分类] 数学（综合）

[关键词] Differential quadrature;Riccati differential equation;Chebyshev polynomial;Caputo derivative