218925167620+ / 218919656575+ / 218916307390+ / 218911653137+
95 / 2020
دار الكتب الوطنية بنغازي
BERNOULLI DIFFERENTIAL EQUATION OF SECOND ORDER
WITH FRACTIONAL DERIVATIVE
تاريخ الاستلام: 15-10-2020م
تاريخ التقييم: 25-10-2020م
Pages:1-17
Mufeedah Maamar Salih Ahmed
في هذه الدراسة ، نقدم معادلة غير خطية من الدرجة الثانية مع اللاخطية من نوع برنولي ، والتي تشمل مشتقات الرتبة الكسرية. نحن نعتبر الحل العددي للمعادلة غير الخطية باستخدام طريقة التكرار Picard ، وتسعى الطريقة لفحص تقارب الحلول لهذا النوع من المعادلات. أظهر الحل الناتج أنه يمكن زيادة التقارب في كل مستوى تكرار. ومع ذلك ، مع زيادة عدد التكرارات ، هناك معدل تقارب سريع للحل التقريبي مع الحل التحليلي. جميع النتائج التي تم الحصول عليها باستخدام طريقة Picard الكلاسيكية في المعادلة وتمت مقارنتها مع الحل الدقيق.
الكلمات المفتاحية: المشتقات الكسرية ، معادلة برنولي التفاضلية من الدرجة الثانية ، طريقة التكرار بيكارد.
In this study, we present a second order nonlinear equation with nonlinearity of Bernoulli type, which include fractional order derivatives. We consider the numerical solution of the nonlinear equation using the Picard iteration method, the method seeks to examine the convergence of solutions of this type of equations. The resulting solution showed that the convergence could be increased at each iterate level. However, as the number of iterations increases, there is a rapid rate of convergence of the approximate solution to the analytic solution. All Results obtained with the classical Picard method on the equation and were compared with the exact solution.
Keywords: Fractional derivatives, Bernoulli differential equation of second order, Picard iteration method.
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