Treffer: NUMERICAL SOLUTION OF FOKKER-PLANCK-KOLMOGOROV TIME FRACTIONAL DIFFERENTIAL EQUATIONS USING LEGENDRE WAVELET METHOD ALONG WITH CONVERGENCE AND ERROR ANALYSIS.

The aim of this paper is to numerically solve the Fokker-Planck-Kolmogorov fractional-time differential equations using the Legendre wavelet. Also, we analyzed the convergence of function approximation using Legendre wavelets. Introduced the absolute value between the exact answer and the approximate answer obtained by the given numerical methods, and analyzed the error of the numerical method. This method has the advantage of being simple to solve. The results revealed that the suggested numerical method is highly accurate and effective. The results for some numerical examples are documented in table and graph form to elaborate on the efficiency and precision of the suggested method. The simulation was carried out using MATLAB software. In this paper and for the first time, the authors presented results on the numerical simulation for classes of time-fractional differential equations. The authors applied the reproducing Legendre wavelet method for the numerical solutions of nonlinear Fokker-Planck-Kolmogorov time-fractional differential equation. The method presented in the present study can be used by programmers, engineers, and other researchers in this field. [ABSTRACT FROM AUTHOR]

المقال يناقش الحل العددي لمعادلات فوكير-بلانك-كولموغوروف التفاضلية الزمنية الكسرية باستخدام طريقة الموجات ليجاندر، مع التركيز على فعاليتها ودقتها. يقدم أمثلة عددية من خلال الجداول والرسوم البيانية، مما يوضح كفاءة الطريقة في حل المعادلات الكسرية التكاملية-التفاضلية ذات النوى الضعيفة الانفراد. البحث، الذي أجراه علماء من جامعة شهروود للتكنولوجيا في إيران، يستخدم برنامج MATLAB للمحاكاة، مما يبرز التطبيق العملي للنهج للباحثين والمهندسين. تم نشر النتائج في المجلة المفتوحة الوصول "نمذجة رياضية تطبيقية"، مما يسمح بزيادة الوصول تحت رخصة المشاع الإبداعي النسبية-غير التجارية 4.0 الدولية. [Extracted from the article]

Copyright of Journal of Advanced Mathematical Modeling (JAMM) is the property of Shahid Chamran University of Ahvaz and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)