AWhat changed
Crank and Nicolson develop a time-centred implicit finite-difference procedure for heat-conduction-type equations, combining a stable linear error treatment with practical iteration for nonlinear terms and boundary conditions.
Scientific scope
Crank and Nicolson develop a time-centred implicit finite-difference procedure for heat-conduction-type equations, combining a stable linear error treatment with practical iteration for nonlinear terms and boundary conditions. The centered implicit discretization and nonlinear iterative solve are separate parts of the method. The original error analysis concerns the stated linear heat equation and boundary/symmetry conditions, not universal nonlinear convergence. Large steps can yield slowly decaying oscillations and need not preserve positivity. Singular starting gradients require special treatment. The reviewed source is a permissioned later reprint/transcription of the 1947 work. Reported mesh comparisons and computational costs have not been independently replayed by WRS.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- J. Crank · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- P. Nicolson · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- J. Crank and P. Nicolson, practical heat-conduction numerical method — complete 1996 permissioned reprint of 1947 work, web OCRtranscription
- Publisher reprint notice and twoauthorbyline for Crank/Nicolson original 1947 work
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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