کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4638225 | 1631999 | 2016 | 25 صفحه PDF | دانلود رایگان |
We exhibit an algorithm which computes an ϵϵ-approximation of the positive solutions of a family of boundary-value problems with Neumann boundary conditions. Such solutions arise as the stationary solutions of a family of semilinear parabolic equations with Neumann boundary conditions. The algorithm is based on a finite-dimensional Newton iteration associated with a suitable discretized version of the problem under consideration. To determine the behavior of such a discrete iteration we establish an explicit mesh-independence principle. We apply a homotopy-continuation algorithm to compute a starting point of the discrete Newton iteration, and the discrete Newton iteration until an ϵϵ-approximation of the stationary solution is obtained. The algorithm performs roughly O((1/ϵ)1/2)O((1/ϵ)1/2) flops and function evaluations.
Journal: Journal of Computational and Applied Mathematics - Volume 292, 15 January 2016, Pages 188–212