Numerical Verification of Solutions for Nonlinear Parabolic Problems

被引：4

作者：

Hashimoto, Kouji ^{[1
]}

Kinoshita, Takehiko ^{[2
]}

Nakao, Mitsuhiro T. ^{[3
]}

机构：

[1] Nakamura Gakuen Jr Coll, Div Infant Educ, Fukuoka, Japan

[2] Kyushu Univ, Res Inst Informat Technol, Fukuoka, Japan

[3] Waseda Univ, Fac Sci & Engn, Tokyo, Japan

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2020年 / 41卷 / 12期

关键词：

Nonlinear parabolic problems; numerical verification method; partial differential equations; EQUATIONS;

D O I：

10.1080/01630563.2020.1777159

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a numerical verification method of solutions for nonlinear parabolic initial boundary value problems. Decomposing the problem into a nonlinear part and an initial value part, we apply Nakao's projection method, which is based on the full-discrete finite element method with constructive error estimates, to the nonlinear part and use the theoretical analysis for the heat equation to the initial value part, respectively. We show some verified examples for solutions of nonlinear problems from initial value to the neighborhood of the stationary solutions, which confirm us the actual effectiveness of our method.

引用

页码：1495 / 1514

页数：20

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