حل عددی دستگاه معادلات غیرخطی با الگوریتم فراابتکاری ARO بهبودیافته | ||
| محاسبات نرم | ||
| دوره 14، شماره 1 - شماره پیاپی 27، شهریور 1404، صفحه 184-203 اصل مقاله (919.53 K) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22052/scj.2025.254888.1244 | ||
| نویسندگان | ||
| علی حمدی پور؛ عبدالعلی بصیری* ؛ مصطفی زارع | ||
| دانشکده ریاضی و علوم کامپیوتر، دانشگاه دامغان، دامغان، ایران. | ||
| چکیده | ||
| حل دستگاه معادلات غیرخطی یکی از سختترین مسائل در محاسبات عددی است. روشهای عددی سنتی مانند روشهای نیوتن و انواع آن نیاز به حدس اولیه خوب برای حل دستگاه معادلات غیرخطی دارند. حدس اولیه نامناسب میتواند تاثیر سوء در عملکرد و همگرایی این روشها داشته باشد. در عمل، دستیابی به این حدس اولیه دشوار و از نظر زمانی پرهزینه خواهد بود. با هدف غلبه بر این مشکل، در این مقاله بهرهگیری از الگوریتم فراابتکاری بهبودیافته (IARO) برای حل عددی دستگاه معادلات غیرخطی پیشنهاد شده است. از آنجا که حل دستگاه معادلات غیرخطی را میتوان به حل یک مساله بهینهسازی تقلیل داد، الگوریتم فراابتکاری توانایی خوبی در پیدا کردن جواب آن خواهد داشت. الگوریتم فراابتکاری ARO از رفتار خرگوشها در هنگام تغذیه الگو گرفته است و میتواند مسائل بهینهسازی پیچیده را در زمان مناسب حل کند. در روش پیشنهاد شده، الگوریتم ARO به کمک جدول حافظه بهبود یافته تا عملکرد مناسبی برای حل دستگاه معادلات غیرخطی داشته باشد. برای سنجش عملکرد روش پیشنهاد شده، جواب چندین دستگاه معادلات غیرخطی پیچیده توسط آن محاسبه شده که نتایج آن عملکرد خوب روش پیشنهادی را نمایش میدهد. | ||
| کلیدواژهها | ||
| دستگاه معادلات غیرخطی؛ آنالیز عددی؛ الگوریتمهای فراابتکاری؛ الگوریتم ARO؛ بهینهسازی | ||
| مراجع | ||
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