روش محاسباتی برای حل معادلات دیفرانسیل تصادفی تأخیری از مرتبه کسری
الموضوعات :بهروز پارسا مقدم 1 , زینب سلامت مستقیم 2 , الهام السادات هاشمی زاده 3
1 - گروه ریاضی، دانشکده علوم ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران
2 - گروه ریاضی، دانشکده علوم ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران
3 - گروه ریاضی، واحد کرج، دانشگاه آزاد اسلامی، کرج، ایران
الکلمات المفتاحية: Fractional calculus, Stochastic calculus, Bilinear spline interpolation, Stochastic delay differential equations,
ملخص المقالة :
سیستم های دینامیکی در بسیاری از شاخه های علوم و صنعت غالبا با انواع مختلف از نویزهای محیطی آشفته می شوند. آنالیز این سیستم ها از اهمیت ویژه ای مابین پژوهشگران برخودار می باشند. در این مقاله، ما روشی برای محاسبه جواب تقریبی معادلات دیفرانسیل غیر خطی تصادفی تاخیری از مرتبه کسری حاصل از حرکت برآونی را ارائه می‌دهیم. مشتقات از مرتبه کسری از نوع کاپوتو در نظر گرفته شده است. اساس روش محاسباتی بر پایه درون‌یابی اسپلاین دو خطی و تقریب تفاضلات متناهی می باشد. مرتبه همگرایی روش پیشنهادی با استفاده از نرم میانگین مجذور اثبات شده است و دقت روش از منظر میانگین خطای مطلق و مرتبه همگرایی تجربی آنالیز شده است. روش ارایه شده برای تعیین شاخص‌های آماری در مدل‌های گومبرتزیان و نیکولسون بکار گرفته شده است. معادله دیفرانسیل تاخیری و تصادفی گومبرتزیان از مرتبه کسری مدلسازی شده است برای توصیف رشد فرایند سرطان و معادله دیفرانسیل تاخیری و تصادفی نیکولسون از مرتبه کسری برای بیان دینامیک جمعیت آشفتگی های نیکولسون در محیط زیست، فرموله شده است.
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