On the numerical solution of the diffusion equation
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- by Øystein Tødenes PDF
- Math. Comp. 24 (1970), 621-627 Request permission
Abstract:
A proof given by C. E. Pearson $[1]$ for the asymptotic convergence of the numerical solution of the diffusion equation is discussed, and found insufficient. A new, direct proof is given. A method given by Pearson, for improving the numerical solution when a discontinuity is present in the initial-boundary conditions, is considered in more detail.References
- Carl E. Pearson, Impulsive end condition for diffusion equation, Math. Comp. 19 (1965), 570–576. MR 193765, DOI 10.1090/S0025-5718-1965-0193765-5
- H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford, at the Clarendon Press, 1947. MR 0022294
- I. B. Parker and J. Crank, Persistent discretization errors in partial differential equations of parabolic type, Comput. J. 7 (1964), 163–167. MR 183126, DOI 10.1093/comjnl/7.2.163
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Math. Comp. 24 (1970), 621-627
- MSC: Primary 65.68
- DOI: https://doi.org/10.1090/S0025-5718-1970-0275702-X
- MathSciNet review: 0275702