High accuracy stable numerical solution of ID microscale heat transport equation

Jun Zhang, Jennifer J. Zhao

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We investigate the use of a fourth-order compact finite difference scheme for solving a one-dimensional heat transport equation at the microscale. The fourth-order compact scheme is used with a Crank-Nicholson type integrator by introducing an intermediate function for the heat transport equation. The new scheme is proved to be unconditionally stable with respect to initial values. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second-order spatial discretization. It is shown that the new scheme is computationally more efficient and more accurate than the second-order scheme.

Original languageEnglish
Pages (from-to)821-832
Number of pages12
JournalCommunications in Numerical Methods in Engineering
Issue number11
StatePublished - Nov 2001


  • Crank-Nicholson integrator
  • Finite difference
  • Fourth-order compact scheme
  • Heat transport equation

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • General Engineering
  • Computational Theory and Mathematics
  • Applied Mathematics


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