Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case

Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case In this paper, we describe a numerical method to verify the solutions with guaranteed error bounds for nonlinear parabolic problems in one dimensional case. It is based on Plum's method for formulating the problem and weak formulation for estimating explicitly the inverse norm of the linearized operator. We introduce some weighted norms on time-dependent Sobolev spaces, which play an important role in the application of our method. We present detailed verification procedures by using this weighted norm and show some numerical examples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1997 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009933805322
Publisher site
See Article on Publisher Site

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