Unconditionally Stable Finite Difference Scheme and Iterative Solution of 2D Microscale Heat Transport Equation

Jun Zhang, Jennifer J. Zhao

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


A two-dimensional time-dependent heat transport equation at the microscale is derived. A second order finite difference scheme in both time and space is introduced and the unconditional stability of the finite difference scheme is proved. A computational procedure is designed to solve the discretized linear system at each time step by using a preconditioned conjugate gradient method. Numerical results are presented to validate the accuracy of the finite difference scheme and the efficiency of the proposed computational procedure.

Original languageEnglish
Pages (from-to)261-275
Number of pages15
JournalJournal of Computational Physics
Issue number1
StatePublished - Jun 10 2001

Bibliographical note

Funding Information:
1URL: http://www.cs.uky.edu/˜jzhang. The research of this author was supported in part by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0043861, and in part by the University of Kentucky Center for Computational Sciences. 2URL: http://www.umd.umich.edu/˜xich.


  • Crank-Nicholson integrator
  • Finite difference scheme
  • Heat transport equation
  • Preconditioned conjugate gradient

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy (all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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