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رقم الإيداع المحلي
95 / 2020
دار الكتب الوطنية بنغازي
ISSN: 2706-9087
المجلد السادس
العدد الحادي عشر لشهر يونيو 2021

رجوع

NUMERICAL SOLUTIONS OF BERNOULLI DIFFERENTIAL EQUATIONS WITH FRACTIONAL DERIVATIVES BY RUNGE-KUTTA TECHNIQUES

تاريخ الاستلام: 22-3-2021م

تاريخ التقييم: 24-3-2021م

Pages:272-288

Mufeedah Maamar Salih Ahmed
الملخص:

ناقشنا في هذه الدراسة الحلول العددية لمسألة القيمة الأولية للمعادلة برنولي اللاخطية من الرتبة الثانية مع المشتق الكسري و طريقة ايجاد الحل العددي لها باستخدام طريقتي Runge-Kutta من الرتبة الرابعة و Runge-Kutta المعدلة وبالإضافة إلي طريقة Runge-Kutta Mersian و من ثمَّ مقارنة الحل بالحل المضبوط.
الكلمات المفتاحية: معادلة برنولي مع المشتقات الكسرية، مشكلة القيمة الأولية، طرق رونج-كوتا، طرق رونج-كوتا المعدلة وطرق رونج-كوتا ميرسيان.

Abstract:

In this article, we discussed the numerical solution of Brnoulli's equation with fractional derivatives subject to initial value problems by applying 4th order Runge-Kutta, modified Runge-Kutta and Runge-Kutta Mersian methods. Here the solutions of some numerical examples have been obtained with the help of mathematica program as well as we determined the exact analytic solutions.
Keywords: Bernoulli equation with fractional derivatives, Initial value problem, Runge-Kutta, Modified Runge-Kutta and Runge-Kutta Mersian Methods.

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