بررسی عددی یک طرح تفاضلی برای معادلات انتشار کسری زمانی- مکانی کپوتو- ریس چندجمله‌ای
الموضوعات :مجتبی فردی 1 , ابراهیم امینی 2
1 - گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه شهرکرد، صنوق پستی 88186-34141، شهرکرد، ایران
2 - گروه ریاضی، دانشگاه پیام نور، صندوق پستی ۴۶٩٧- ١٩٣٩۵، تهران، ایران
الکلمات المفتاحية: Fractional diffusion equations, Caputo-Riesz derivative, Convergence, stable Conditionally, Difference scheme,
ملخص المقالة :
چکیده: در این مقاله، یک طرح تفاضلی برای حل معادلات انتشار کسری زمانی- مکانی چند جمله‌ای ارائه می‌شود. در معادلات انتشار کسری، مشتق زمانی از نوع کپوتو چند جمله‌ای و مشتق مکانی از نوع ریس هستند. معادلات مذکور در بعدهای یک و دو در نظر گرفته شده‌اند. در بعد یک مشتق مکانی ریس از مرتبه‌ی و در بعد دو مشتق مکانی ریس از مرتبه‌های و هستند. هم‌چنین، مشتق کپوتو چند جمله‌ای از مرتبه‌های هستند. آنالیز پایداری و همگرایی طرح تفاضلی ارائه می‌شود و شرایط پایداری طرح تفاضلی ارائه شده را مورد بررسی قرار می‌دهیم. اثبات می‌کنیم که طرح تفاضلی پیشنهادی پایدار مشروط است. علاوه‌بر‌این نشان می‌دهیم که طرح تفاضلی با مرتبه در زمان و با مرتبه‌ی دو در مکان همگراست. در پایان دو مثال عددی به ترتیب در بعدهای یک و دو داده می‌شود تا کارآیی و قابل اجرا بودن طرح تفاضلی پیشنهادی را از نظر دقت و سرعت همگرایی نشان دهیم.
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