On the numerical solution of the diffusion equation
Math. Comp. 24 (1970), 621-627
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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.
E. Pearson, Impulsive end condition for diffusion
equation, Math. Comp. 19 (1965), 570–576. MR 0193765
(33 #1980), http://dx.doi.org/10.1090/S0025-5718-1965-0193765-5
S. Carslaw and J.
C. Jaeger, Conduction of Heat in Solids, Oxford, at the
Clarendon Press, 1947. MR 0022294
B. Parker and J.
Crank, Persistent discretization errors in partial differential
equations of parabolic type, Comput. J. 7 (1964),
163–167. MR 0183126
- C. E. Pearson, "Impulsive end condition for diffusion equation," Math. Comp., v. 19, 1965, pp. 570-576. MR 33 #1980. MR 0193765 (33:1980)
- H. S. Carslaw & J. C. Jaeger, Conduction of Heat in Solids, Oxford Univ. Press, London, 1959. MR 0022294 (9:188a)
- 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. MR 0183126 (32:608)
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