باز تولید روش نقطه شعاعی بدون شبکه طیفی برای معادله Sobolev با آنالیز خطا
Subject Areas : International Journal of Industrial Mathematicsسعید عباسبندی 1 , الیاس شیوانیان 2
1 - گروه ریاضی، دانشگاه بین المللی قزوین، قزوین، ایران.
2 - گروه ریاضی، دانشگاه بین المللی قزوین، قزوین، ایران.
Keywords: Sobolev equation, Radial point interpolation (RPI), Pseudospectral method, Radial basis function,
Abstract :
در این مطالعه، یک روش تقریبی برای معادلات دو بعدی (2D) Sobolev بر اساس درون یابی نقطه شعاعی بدون شبکه طیفی (PSMRPI) ارایه می شود. معادلات سوبولف که در جریان نفوذ جریان سیال در سنگها، خاکها یا محیطهای مختلف چسبناک مشاهده می شود، به جز در برخی موارد خاص، جواب دقیق ندارند. این مسئله را به سختی می توان حل کرد، به ویژه هنگامی که هندسه دامنه پیچیده تر باشد. در روش PSMRPI، نقاط گره ای نیازی به توزیع منظم ندارند و حتی می توانند کاملاً دلخواه باشند. بوسیله ساخت ماتریس عملیاتی تقریب، مشتقات مرتبه بالا برحسب مقادیر تابع مجهول در نقاط گره ای آسان است. ثابت می کنیم که این روش نسبت به زمان پایداری بی قید و شرط دارد. نتایج اصلی روی معادله سوبولف با چند مثال نشان می دهد که روش PSMRPI قابل اعتماد بوده و خوب عمل می کند.
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