یک روش تفاضلی تکراری با گام‌های متغیر زمانی برای حل عددی مدل نفوذ دارو در سامانه‌های پلیمری کروی

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشکده ریاضی، دانشگاه علم و صنعت ایران

2 دانشگاه پیام نور استان تهران مرکز تهران شرق

چکیده

در این مقاله یک مدل ریاضی نفوذ دارو در سامانه­های دارو رسانی پلیمری کروی مطرح و به‌صورت عددی به حل آن پرداخته‌شده است. مدل مورد بررسی به‌صورت یک مسئله سهموی با کران متحرک و شرایط مرزی غیرخطی است. بر اساس ماهیت غیرخطی مسئله و نیز کران متحرک آن یک روش تفاضلی تکراری با طول گام متغیر زمانی برای نخستین بار برای حل مسئله پیشنهاد شده است و الگوریتم روش به‌صورت کامل ارائه‌شده است. به دلیل عدم دسترسی به فرم جواب مسئله و برای درک بهتر عملکرد روش، نتایج عددی حاصل با جواب­های مجانبی و نتایج موجود در منبع [14] مقایسه شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

An Iterative Finite Difference Approach with Time Variable Steps for the Numerical Investigation of the Model of Drug Diffusion Through Polymeric Spheres

نویسندگان [English]

  • Morteza Garshasbi 1
  • Parastoo Reihani Ardabili 2
1 School of Mathematics, Iran University of Science and Technology, Tehran, Iran
2 Payame Noor University of Tehran, Tehran Shargh Unit, Iran
چکیده [English]

In this paper, a mathematical model of drug diffusion in spherical polymeric drug delivery devices is considered and investigated numerically. The proposed model considered as a moving boundary parabolic equation with nonlinear condition at the moving boundary. Because of the nonlinearity of the problem and existence of a moving boundary in proposed problem, a new iterative finite differences approach with time variable steps is established to solve this problem. The closed form of solution of the proposed problem has not been derived and to show the ability of the method, the numerical results have been compared with asymptotic solutions and the results of the paper [14].

کلیدواژه‌ها [English]

  • Drug diffusion
  • moving boundary problem
  • Finite difference method
  • variable time step
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