document: Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation This paper is concerned with the stability constant C/sub infinity / in the maximum-norm of the Crank-Nicolson scheme applied . to the one-dimensional heat equation . A well known result due to S.J. Serdyukova is that C/sub infinity / < 23 . In the present paper , by using a sharp resolvent estimate for the discrete Laplacian together with the Cauchy formula , it is shown that 3 < or = C/sub infinity / < 4.325 . This bound also holds when the heat equation is considered on a bounded interval along with Dirichlet or Neumann boundary conditions
doc_bio_tags: 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 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 O O O O O O O O O O O B I I O O B I 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 O O B I I
extractive_keyphrases: stability constant sharp resolvent estimate discrete laplacian cauchy formula neumann boundary conditions
abstractive_keyphrases: crank-nicolson scheme one-dimensional heat equation dirichlet boundary conditions