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

Document Type : Research Paper

Authors

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

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations
Volume 14, Issue 1
January 2026
Pages 81-94

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History

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

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