روشی بدون شبکه برای حل عددی مدل ریاضی از مرتبه مشتق کسری تشکیل مویرگ در تومور رگزایی

نوع مقاله: مقاله پژوهشی

نویسندگان

گروه ریاضی، دانشگاه لرستان

چکیده

این مقاله به حل عددی مدل تومور رگزایی با مشتقات از مرتبه کسری می پردازد. بعد از معرفی، مدل را ساده کرده و مدل حاصله را با گسسته سازی زمانی با مشتق کسری وزندار دو سطر زمانی متوالی و با استفاده از توابع پایه ای شعاعی تقریب زده می شود. همچنین همگرایی و پایداری تقریب را تحلیل نموده و برخی حالات عددی نیز مورد بررسی قرار گرفته است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Meshfree method for solving mathematical fractional order model of capillary formation in tumor angiogenesis

نویسندگان [English]

  • Bahman Ghazanfari
  • Amin Shahkarami
Department of Mathematics, Lorestan University
چکیده [English]

This paper was devoted to numerical solution of capillary formation in tumor angiogenesis with time fractional derivative. A time discretization approach based on the θ-weighted fractional finite difference scheme was employed for time fractional derivative and a mesh free process was applied by using radial basis functions (RBFs). Stability analysis of the method was also investigated and some numerical cases were studied.

کلیدواژه‌ها [English]

  • Meshfree method
  • Radial basis functions
  • Fractional derivative
  • Tumor angiogenesis
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