Academic Journal

A Novel Numerical Method for Solving Nonlinear Fractional-Order Differential Equations and Its Applications

التفاصيل البيبلوغرافية
العنوان: A Novel Numerical Method for Solving Nonlinear Fractional-Order Differential Equations and Its Applications
المؤلفون: Seyeon Lee, Hyunju Kim, Bongsoo Jang
المصدر: Fractal and Fractional, Vol 8, Iss 1, p 65 (2024)
بيانات النشر: MDPI AG
سنة النشر: 2024
المجموعة: Directory of Open Access Journals: DOAJ Articles
مصطلحات موضوعية: Atangana–Baleanu fractional derivative, fractional differential equations, predictor-corrector methods, sum-of-exponentials approximation, sub-diffusion equation, Thermodynamics, QC310.15-319, Mathematics, QA1-939, Analysis, QA299.6-433
الوصف: In this article, a considerably efficient predictor-corrector method (PCM) for solving Atangana–Baleanu Caputo (ABC) fractional differential equations (FDEs) is introduced. First, we propose a conventional PCM whose computational speed scales with quadratic time complexity O ( N 2 ) as the number of time steps N grows. A fast algorithm to reduce the computational complexity of the memory term is investigated utilizing a sum-of-exponentials (SOEs) approximation. The conventional PCM is equipped with a fast algorithm, and it only requires linear time complexity O ( N ) . Truncation and global error analyses are provided, achieving a uniform accuracy order O ( h 2 ) regardless of the fractional order for both the conventional and fast PCMs. We demonstrate numerical examples for nonlinear initial value problems and linear and nonlinear reaction-diffusion fractional-order partial differential equations (FPDEs) to numerically verify the efficiency and error estimates. Finally, the fast PCM is applied to the fractional-order Rössler dynamical system, and the numerical results prove that the computational cost consumed to obtain the bifurcation diagram is significantly reduced using the proposed fast algorithm.
نوع الوثيقة: article in journal/newspaper
اللغة: English
تدمد: 2504-3110
Relation: https://www.mdpi.com/2504-3110/8/1/65; https://doaj.org/toc/2504-3110; https://doaj.org/article/af6645e53d304060bf78ba51ede6f59b
DOI: 10.3390/fractalfract8010065
الاتاحة: https://doi.org/10.3390/fractalfract8010065
https://doaj.org/article/af6645e53d304060bf78ba51ede6f59b
رقم الانضمام: edsbas.50DFF834
قاعدة البيانات: BASE
الوصف
تدمد:25043110
DOI:10.3390/fractalfract8010065