Numerical Verification of Solutions for Nonlinear Parabolic Problems. (9th September 2020)

• Record Type: Journal Article
• Authors: Hashimoto, Kouji; Kinoshita, Takehiko; Nakao, Mitsuhiro T.
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 12(2020)
• Page Start: 1495
• Page End: 1514
• Publication Date: 2020-09-09
• Subjects: Nonlinear parabolic problems -- numerical verification method -- partial differential equations; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1777159
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: 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.