روش ماتریسی جدید برای حل تقریبی یک مدل جدید لین-اِمدن منفرد

نوع مقاله : مقاله پژوهشی

نویسنده

گروه ریاضی کاربردی، دانشکده ریاضی و کامپیوتر، دانشگاه شهید باهنر کرمان، کرمان، ایران

چکیده

مطالعه حاضر به یافتن جواب های تقریبی یک مدل جدید از دستگاه معادلات لین-اِمدن منفرد غیرخطی مرتبه دوم با شرایط مرزی اختصاص داده شده است. روش ماتریسی پیش نهادی ما بر اساس توابع چلیشکوف به همراه نقاط هم محلی است تا دستگاه غیرخطی را به یک معادله ماتریس اساسی جبری تبدیل کند. هم گرایی روش طیفی چلیشکوف نیز اثبات شده است. برای نشان دادن کارایی و دقت روش ارائه شده، سه مثال بصورت عددی حل شده است. همچنین، مقایسه هایی با جواب های دقیق و با یک روش موجود در منابع انجام شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A novel matrix technique to solve a new singular nonlinear functional Lane-Emden model

نویسنده [English]

  • Mohammad Izadi
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
چکیده [English]

The present study is devoted to finding the approximate solutions of a new design of a second-order nonlinear functional system of Lane-Emden differential equation with boundary conditions. Our proposed matrix technique is based on the Chelyshkov functions together with collocation points to transform the nonlinear system into an algebraic fundamental matrix equation. The convergence of the spectral Chelyshkov approach is also proved. To show the efficiency and the accuracy of the presented technique, three test examples are solved numerically. Also, comparisons with the exact solutions and with an available method in the literature are performed.

کلیدواژه‌ها [English]

  • Chelyshkov functions
  • Collocation points
  • Functional differential equation
  • Singular Lane-Emden system
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