کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4641492 1341310 2010 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Approximation of the solution of certain nonlinear ODEs with linear complexity
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Approximation of the solution of certain nonlinear ODEs with linear complexity
چکیده انگلیسی

We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the “continuous” equation. Furthermore, we exhibit an algorithm computing an εε-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 233, Issue 9, 1 March 2010, Pages 2339–2350
نویسندگان
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