document: Construction of two-sided bounds for initial-boundary value problems This paper extends the bounding operator approach developed for boundary value problems to the case of initial-boundary value problems -LRB- IBVPs -RRB- . Following the general principle of bounding operators enclosing methods for the case of partial differential equations are discussed . In particular , continuous discretization methods with an appropriate error bound controlled shift and monotone extensions of Rothe 's method for parabolic problems are investigated
doc_bio_tags: O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O B I O O
extractive_keyphrases: bounding operator approach bounding operators partial differential equations parabolic problems
abstractive_keyphrases: two-sided bounds initial-boundary value problems