On the numerical solution of the diffusion equation
Abstract: A proof given by C. E. Pearson $$ 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.
- Carl E. Pearson, Impulsive end condition for diffusion equation, Math. Comp. 19 (1965), 570–576. MR 193765, DOI https://doi.org/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 https://doi.org/10.1093/comjnl/7.2.163
C. E. Pearson, "Impulsive end condition for diffusion equation," Math. Comp., v. 19, 1965, pp. 570–576. MR 33 #1980.
H. S. Carslaw & J. C. Jaeger, Conduction of Heat in Solids, Oxford Univ. Press, London, 1959.
I. B. Parker & J. Crank, "Persistent discretization errors in partial differential equations of parabolic type," Comput. J., v. 7, 1964, pp. 163–167. MR 32 #608.
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