موجک‌های لژاندر برای حل عددی دستگاهی از معادلات شرودینگر دوبعدی غیرخطی کسری- فراکتالی

Document Type : Research Paper

Authors

1 بخش ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه یزد، استان یزد، ایران

2 گروه ریاضی کاربردی، دانشکده ریاضی، دانشگاه صنعتی شیراز، استان فارس، ایران

10.22072/wala.2020.119323.1263

Abstract

در این  مقاله، یک روش نیمه‌گسسته بر اساس موجک‌های لژاندر دوبعدی  را برای به‌دست آوردن جواب‌های تقریبی دستگاهی از معادلات شرودینگر غیرخطی کسری فراکتالی ارایه می‌دهیم. با وجود اینکه روش پیشنهادی  را می‌توان برای هر  نوع مشتق کسری (هسته نامنفرد) به‌کار برد،
 ولی  در این مقاله روی مشتق ریمان- لیوویل- آتانگانا با هسته نامنفرد میتاگ- لفلر تمرکز می‌کنیم.   در این راستا ابتدا مشتقات کسری- فراکتال زمانی توسط روش تفاضلات متناهی تقریب زده می‌شوند. سپس از روش  تفاضلات متناهی وزن‌دار شده با پارامتر تتا  برای به‌دست آوردن رابطه بازگشتی مساله استفاده می‌شود.

Keywords


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