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Mathematics of Computation

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On the numerical solution of the diffusion equation

Author: Øystein Tødenes
Journal: Math. Comp. 24 (1970), 621-627
MSC: Primary 65.68
MathSciNet review: 0275702
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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 [Enhancements On Off] (What's this?)

  • [1] C. E. Pearson, "Impulsive end condition for diffusion equation," Math. Comp., v. 19, 1965, pp. 570-576. MR 33 #1980. MR 0193765 (33:1980)
  • [2] H. S. Carslaw & J. C. Jaeger, Conduction of Heat in Solids, Oxford Univ. Press, London, 1959. MR 0022294 (9:188a)
  • [3] 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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Keywords: Asymptotic convergence, stationary solution, singular boundary conditions
Article copyright: © Copyright 1970 American Mathematical Society

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