On the Smoothing Property of the Crank-Nicolson Scheme

Mitchell Luskin

doi:10.1080/00036818208839415

On the Smoothing Property of the Crank-Nicolson Scheme

Mitchell Luskin

School of Mathematics

Research output: Contribution to journal › Article › peer-review

88 Scopus citations

Abstract

The Crank-Nicolson scheme for discretizing linear parabolic equations converges at the rate of only o(1) in L2 for initial data in L2. It is shown that smoothing by adding four backward Euler steps to the scheme improves the convergence rate to 0{k2/t2).

Original language	English (US)
Pages (from-to)	117-135
Number of pages	19
Journal	Applicable Analysis
Volume	14
Issue number	2
DOIs	https://doi.org/10.1080/00036818208839415
State	Published - Jan 1 1982

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title = "On the Smoothing Property of the Crank-Nicolson Scheme",

abstract = "The Crank-Nicolson scheme for discretizing linear parabolic equations converges at the rate of only o(1) in L2 for initial data in L2. It is shown that smoothing by adding four backward Euler steps to the scheme improves the convergence rate to 0{k2/t2).",

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AB - The Crank-Nicolson scheme for discretizing linear parabolic equations converges at the rate of only o(1) in L2 for initial data in L2. It is shown that smoothing by adding four backward Euler steps to the scheme improves the convergence rate to 0{k2/t2).

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On the Smoothing Property of the Crank-Nicolson Scheme

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