کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6423141 1341248 2011 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Solving boundary value problems for delay differential equations by a fixed-point method
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Solving boundary value problems for delay differential equations by a fixed-point method
چکیده انگلیسی

A general linear boundary value problem for a nonlinear system of delay differential equations (DDE in short) is reduced to a fixed-point problem v=Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by piecewise linear function vh defined by its values vi=vh(ti) at grid points ti, i=0,1,…,N, where N is a given positive integer and h=max1≤i≤N(ti−ti−1). Under suitable assumptions, the existence of a fixed-point of A is equivalent to existence of so called ε(h)-approximate fixed-points of vh=Avh, which can be found by minimization of L2(n) norm of residuum vh−Avh with respect to the variables vi. These ε(h)-approximate fixed-points are used for obtaining approximate solutions of the original boundary value problem for a system of DDE. Numerical experiments with the boundary value problem for a system of delay differential equations of population dynamics as well as with two periodic boundary value problems: one for the periodic distributed delay Lotka-Volterra competition system and the second one modeling two coupled identical neurons with time-delayed connections show an efficiency of this kind of approach.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 6, 15 October 2011, Pages 1576-1590
نویسندگان
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