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.
Reliable Computing – Springer Journals
Published: Oct 14, 2004
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
All the latest content is available, no embargo periods.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud