Numerical solution of non-linear fractional Riccati differential equations using compact finite difference method

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 مرداد 1401  

نوع مقاله: SPECIAL ISSUE- Volume 12 No 2 (Summer 2022)

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.76489.1129

نویسندگان

Homayoun Porki؛ Maryam Arabameri ؛ Raziyeh Gharechahi

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

چکیده

This paper aims to apply and investigate the compact finite difference methods for solving integer-order and fractional-order Riccati differential equations. The fractional derivative in the equation is described in the Caputo sense. In solving the Riccati equation, we first approximate 1st order derivative using the approach of compact finite-difference. In this way, the system of nonlinear equations is obtained, which solves the Riccati equation. In addition, we examine the convergence analysis of the proposed approach for the fractional and non-fractional cases and prove the methods are convergent under some suitable conditions. Examples are also given to illustrate our method’s efficiency compared to the other methods.

کلیدواژه‌ها

Fractional Riccati equation؛ Caputo fractional derivative؛ Compact finite difference methods