یک روش تحلیلی بهینه برای حل مسائل مقدار مرزی غیرخطی بر پایه روش تغییر پارامتر
الموضوعات :
1 - گروه ریاضی، دانشگاه آزاد اسلامی، واحد نکا، نکا، ایران
2 - گروه ریاضی، دانشگاه آزاد اسلامی، واحد قائمشهر، قائمشهر، ایران
الکلمات المفتاحية: Optimal variation of parameter, Boundary value problems, Sturm- Liouville, Airy and Quantum mechanical ha,
ملخص المقالة :
در این مقاله، نویسندگان یک الگوریتم تحلیلی همگرای اصلاح شده را برای جواب مسائل مقدار مرزی و مقدار اولیه غیرخطی به واسطه روش تغییر پارامتر ارائه میکنند و بطور خلاصه روش تغییر پارامتر بهینه مینامند. این روش براساس تعبیه یک پارامتر و یک عملگر کمکی، یک مزیت محاسباتی برای همگرایی جوابهای تقریبی معادلات دیفرانسیل غیرخطی مهیا میکند. همگرایی توسعه یافته مذ کور نشان داده شده و جزییات آن نیز مورد بحث قرار میگیرد. علاوه بر این، یک روش مناسب برای انتخاب مقدار بهینه پارامتر کمکی در نظر گرفته میشود که تحت مینیممسازی خطا روی دامنه مساله میباشد. موثر بودن روش و دقت الگوریتم پیشنهادی، با اجرا روی مسائل فیزیکی همچون مساله استورم- لیوویل، مساله ایری و مساله نوسانگر هارمونیک کوانتومی نشان داده میشود. نتایج عددی و شکلهای بدست آمده بوضوح دقت الگوریتم و همگرایی آن را منعکس میکند.
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