Numerical verification method for positive solutions of elliptic problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:370

Article

Tanaka, Kazuaki¹ 

[1] Waseda Univ, Inst Math Sci, Shinjyuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

关键词: Computer-assisted proof;    Elliptic problems;    Newton's method;    Numerical verification;    Positive solutions;    Verified numerical computation;   

DOI  :  10.1016/j.cam.2019.112647

来源: Elsevier

【 摘 要 】

The purpose of this paper is to propose methods for verifying the positivity of a weak solution u of an elliptic problem assuming H-0(1)-error estimation parallel to u - (u) over cap parallel to(H01) <= rho given some numerical approximation (u) over cap and an explicit error bound rho. We provide a sufficient condition for the solution to be positive and analyze the range of application of our method for elliptic problems with polynomial nonlinearities. We present numerical examples where our method is applied to some important problems. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free