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.
|出版ステータス||Published - 1997|
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