شیوه‌‌های خوب (و نه‌‌چندان خوب) در روش‌‌های محاسباتی برای حسابان کسری

نوع مقاله : مقاله ترجمه ای

نویسنده

گروه ریاضی، دانشگاه کردستان، سنندج، ایران

چکیده

حل معادلات دیفرانسیل مرتبه کسری در بیشتر موارد نیازمند استفاده از رویکردهایی محاسباتی است. به‌طور کلی، بحث عددی معادلات دیفرانسیل کسری بسیار دشوارتر از حالت مرتبۀ صحیح آن است، و بیشتر اوقات پژوهشگران غیرمتخصص از دشواری‌های خاص آن بی‌اطلاع‌اند. در نتیجه، روش‌های عددی معمولاً به شیو‌ه‌ای نادرست به‌کار برده می‌شوند یا روش‌های غیرقابل‌اعتماد در نوشتجات ابداع و پیشنهاد می‌شوند. در این مقاله سعی می‌کنیم برخی چالش‌های مشترک در استفاده از روش‌های عددی در حسابان کسری را شناسایی، ماهیت آنها را تشریح و چند شیوۀ خوب برای حصول به نتایج درست معرفی کنیم.

کلیدواژه‌ها

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