COMPACT FINITE DIFFERENCE SCHEME FOR NUMERICAL SOLUTION OF CAPUTO-FABRIZIO FRACTIONAL RICCATI DIFFERENTIAL EQUATIONS

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, 98155-987, Iran.

Abstract

Riccati differential equation (RDE) is a kind of non-linear differential equation that has been 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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 18 January 2025

Files

History

  • Receive Date: 06 March 2024
  • Revise Date: 04 January 2025
  • Accept Date: 13 January 2025

Share

How to cite

Statistics