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A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type
Abstract
This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equation where subject to the boundary conditions A, k, q are known constants. Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).
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Metadata
- Authors
- Crank, J., & Nicolson, P.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1947-01
- Volume
- 43
- Issue
- 1
- Pages
- 50-67
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W2167657634
- Cited by
- 3,316
- References
- 0
- FWCI
- 9.34
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. https://app.cochat.ai/papers/10.1017/s0305004100023197
- The paper
- Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/s0305004100023197
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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
