document: Stability in the numerical solution of the heat equation with nonlocal boundary conditions This paper deals with numerical methods for the solution of the heat equation with integral boundary conditions . Finite differences are used for the discretization in space . The matrices specifying the resulting semidiscrete problem are proved to satisfy a sectorial resolvent condition , uniformly with respect to the discretization parameter . Using this resolvent condition , unconditional stability is proved for the fully discrete numerical process generated by applying A -LRB- theta -RRB- - stable one-step methods to the semidiscrete problem . This stability result is established in the maximum norm ; it improves some previous results in the literature in that it is not subject to various unnatural restrictions which were imposed on the boundary conditions and on the one-step methods
doc_bio_tags: B O O B I O O B I O B I I O O O O O O O O O O O B I O B I I O B I O O O O O O O O O B O O O B I O O O O O B I I O O O O O O O O O O O O O O O B O O O O B I I I O O O O O O O O O O O O O B I O O B O O O O O B 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 O O O O O O O
extractive_keyphrases: numerical solution heat equation nonlocal boundary conditions stability integral boundary conditions finite differences matrices semidiscrete problem sectorial resolvent condition fully discrete numerical process maximum norm
abstractive_keyphrases: space discretization one-step methods