Compact finite difference scheme for numerical solution of Caputo-Fabrizio fractional Riccati differential equations

A Riccati differential equation (RDE) is a nonlinear differential equation used in many fields, like Newtonian dynamics, quantum mechanics, stochastic processes, propagation, reactor engineering, and optimal control. In this work, we consider the fractional RDE (FRDE) with the Caputo-Fabrizio derivative and use the compact finite difference scheme to solve it numerically. To solve this equation, we initially approximate the first-order derivative appearing in the definition of the Caputo-Fabrizio derivative through the compact finite difference method. By substituting the obtained approximation formula into the original equation, we derive a system of algebraic equations containing unknown values of the solution of the Riccati equation corresponding to specific discrete points in the domain. Solving this system of non-linear equations yields the solution of the Riccati differential equation at the discrete points. We provide some examples to examine the efficiency and accuracy of the suggested method.

کلیدواژه ها:

Fractional Riccati differential equations ، Caputo-Fabrizio derivative ، Non-linear equations ، Compact finite difference method