یک روش بلوکی هیبریدی شبکه تطبیقی برای حل معادلات دیفرانسیل آشفته تکین غیرخطی

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه کاشان، کاشان، ایران

چکیده

در این مقاله، یک روش عددی موثر برای معادلات دیفرانسیل آشفته تکین غیرخطی مرتبه اول ارائه می‌کنیم. اساس این روش یک روش بلوکی هیبریدی با چهار نقطه بین گامی روی یک شبکه غیریکنواخت است. خواص اصلی روش بلوکی، شامل سازگاری و صفرپایداری و ناحیه پایداری بررسی می‌شوند. به منظور بهینه‌سازی نقاط شبکه از درونیابی و تابع نشانگر طول منحنی استفاده خواهیم کرد. بعد از یافتن شبکه جدید، می‌توان روش بلوکی هیبریدی پیشنهادی را روی شبکه جدید به کار گرفت تا جواب عددی نیز بهینه گردد. نتایج عددی بیانگر دقت و کارایی روش ارائه شده خواهد بود.

کلیدواژه‌ها


عنوان مقاله [English]

An adaptive mesh hybrid block method for solving nonlinear singularly perturbed differential equations

نویسندگان [English]

  • Morteza Bisheh Niasar
  • Alireza Mahdipour
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran.
چکیده [English]

In this paper, we present an efficient numerical method for first order nonlinear singularly perturbed differential equations. This method is based on a hybrid block method with four hybrid points on a non-uniform mesh. The main characteristics of the hybrid block method, including consistency, zero stability and stability region are investigated. In order to optimize mesh points, we will use the interpolation technique and arc-length monitor function. After finding the new optimized mesh points, we can apply the proposed hybrid block method to optimize the numerical solution. The numerical experiments show the efficiency and accuracy of the proposed method.

کلیدواژه‌ها [English]

  • Nonlinear singularly perturbed differential equations
  • Hybrid block method
  • Consistency
  • Zero stability
  • Adaptive mesh
  • Monitor function
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