کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4627385 1631814 2014 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Higher-order time-stepping methods for time-dependent reaction–diffusion equations arising in biology
ترجمه فارسی عنوان
معادلات دیفرانسیل واکنش وابسته به زمان که در زیست شناسی به وجود می آید، روش های زمان گام بالاتر را مرتفع می کنند؟
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی

This paper demonstrates the use of higher order methods to solve some time-dependent stiff PDEs. In the past, the most popular numerical methods for solving system of reaction–diffusion equations was based on the combination of low order finite difference method with low order time-stepping method. We extend in this report the compatibility of fourth-order finite difference scheme (in space) coupled with fourth-order time-stepping methods such as IMEXLM4, IMEXPC4, IMEXRK4 and ETDRK4-B (in time), for direct integration of reaction–diffusion equations in one space dimension. Some interesting numerical anomaly phenomenons associated with steady state solutions of the examples chosen from the literature are well presented to address the naturally arising points and queries. Our findings have led to the understanding of pattern formation such as spiral waves and patchy structures as well as some spatio-temporal dynamical structures.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 240, 1 August 2014, Pages 30–50
نویسندگان
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