استخدام برنامج MATLAB لإيجاد حل تقريبي لمعادلة بولتزمان الحركية لسائل الكتروني
Abstract
تم في هذا البحث حل معادلة بولتزمان الحركية عددياً باستخدام برنامج MATLAB لإيجاد تحولات تابع توزع فرمي ديراك والكثافة الاحتمالية بتابعية كل من درجة الحرارة والسرعة والطاقة الحركية . كما حصلنا على المنحنيات الموافقة لهذه التحولات في فراغ ذي ثلاثة أبعاد دون وضع أية قيود على عبارة الطاقة التي قد تحتوي على بارامترات لانداو من أية مرتبة. ثم قمنا بمقارنة النتائج التي حصلنا عليها مع النتائج المرجعية التي سبق الحصول عليها بطريقة مونت - كارلو (MC) والتي تعتمد على توزع ماكسويل بولتزمان، فوجدنا أن نتائجنا أعم وأكثر دقة، ويمكن الحصول على النتائج المرجعية لطريقة (MC) بأجراء التقريب T→∞ .
This program allows us to find the variation of distribution function
(probability density) as a function of other variables, such as temperature, velocity and kinetic energy. Furthermore to draw the correspondence charts (curves) in space consist of three dimensions without any restrictions on energy which can contain Landau parameters of higher numbers. Comparing these results with the results of Monte-Carlo method (MC), we can conclude that our results are more general if compared with the results in literature, it means that the MATLAB program we used for this purpose is more powerful to solve such problems in comparison to other ones.
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