Numerical solution of nonlinear fractional Riccati differential equations using compact finite difference method

Iranian Journal of Numerical Analysis and Optimization

مقاله 6، دوره 12، Issue 3 (Special Issue) - On the occasion of the 75th birthday of Professor A. Vahidian and Professor F. Toutounian - شماره پیاپی 23، بهمن 2022، صفحه 585-606   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.76489.1129

نویسندگان

H. Porki؛ M. Arabameri^* ؛ R. 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 fractional case is described in the Caputo sense. In solving the Riccati equation, we first approximate first-order derivatives 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 nonfractional cases and prove that the methods are convergent under some suitable conditions. Examples are also given to illustrate the efficiency of our method compared to other methods.
 

کلیدواژه‌ها

Fractional Riccati equation؛ Caputo fractional derivative؛ Com-pact finite difference methods

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