Operational Matrix by Hermite Polynomials for Solving Nonlinear Riccati Differential Equations

Abstract

This paper studies the potential to ensure a numerical solution of nonlinear Riccati differential equations with an effective method, namely operational matrix which is derived by Hermite polynomials with the sense of Caputo derivative. In order to solve the Riccati differential equations, the complete problem is simplified with the operational matrix obtained. To achieve this goal, the proposed approach converts the fractional differential equations (FDEs) into a set of algebraic equations. We then construct a matrix with the algebraic equations and extra equations extracted from initial conditions. Therefore, we achieve the solution by solving these algebraic equations given in a matrix sense. In order to show the efficiency of the proposed idea, we show a number of illustrative examples in which the results confirm the applicability of the suggested approach.