حل معادله کلین–گوردن کسری زمانی فازی با استفاده از ترکیب دو روش تفاضلات متناهی و تبدیل دیفرانسیل کسری | ||
| محاسبات نرم | ||
| دوره 14، شماره 1 - شماره پیاپی 27، شهریور 1404، صفحه 54-71 اصل مقاله (998.4 K) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22052/scj.2024.253677.1191 | ||
| نویسندگان | ||
| زهرا صحرائی؛ مریم عرب عامری* | ||
| گروه ریاضی، دانشکده ریاضی، دانشگاه سیستان و بلوچستان، زاهدان، ایران. | ||
| چکیده | ||
| در این مقاله یک روش ترکیبی برای حل معادله دیفرانسیل کلین ـ گوردن کسری زمانی فازی ارائه میشود. روش مذکور، مبتنی بر ترکیب روشهای تبدیل دیفرانسیل و تفاضلات متناهی است، به این ترتیب که با استفاده از تکنیک نیمه گسستهسازی، ابتدا شاخه پایینی معادله فازی کلین ـ گوردن به یک دستگاه معادلات دیفرانسیل معمولی کسری تبدیل میشود، سپس با استفاده از روش تبدیل دیفرانسیل کسری، دستگاه معادلات دیفرانسیل حاصل حل میشود و جواب شاخه پایینی به دست میآید. در نهایت، با بکارگیری این روند برای شاخه بالایی معادله، جواب تقریبی شاخه بالایی و به دنبال آن، جواب تقریبی معادله کلین ـ گوردن کسری فازی به دست میآید. همگرایی روش مورد بررسی قرار میگیرد و با ارائه مثالهای عددی، نشان داده میشود که این ایده، برای حل معادله فازی کسری از کارایی و دقت قابل قبولی برخوردار است. همچنین زمان اجرای محاسبات نشان میدهد، هزینه محاسباتی آن پایین است. | ||
| کلیدواژهها | ||
| معادله کلین-گوردن کسری فازی؛ روش تبدیل دیفرانسیل کسری؛ روش تفاضلات متناهی؛ جواب تقریبی؛ همگرایی | ||
| مراجع | ||
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