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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations
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by Yingda Cheng, Irene M. Gamba and Jennifer Proft PDF
Math. Comp. 81 (2012), 153-190 Request permission


We develop a high-order positivity-preserving discontinuous Galerkin (DG) scheme for linear Vlasov-Boltzmann transport equations (Vlasov-BTE) under the action of quadratically confined electrostatic potentials. The solutions of such BTEs are positive probability distribution functions and it is very challenging to have a mass-conservative, high-order accurate scheme that preserves positivity of the numerical solutions in high dimensions. Our work extends the maximum-principle-satisfying scheme for scalar conservation laws in a recent work by X. Zhang and C.-W. Shu to include the linear Boltzmann collision term. The DG schemes we developed conserve mass and preserve the positivity of the solution without sacrificing accuracy. A discussion of the standard semi-discrete DG schemes for the BTE are included as a foundation for the stability and error estimates for this new scheme. Numerical results of the relaxation models are provided to validate the method.
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Additional Information
  • Yingda Cheng
  • Affiliation: Department of Mathematics and ICES, University of Texas at Austin, Austin, Texas 78712
  • Address at time of publication: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • MR Author ID: 811395
  • Email:
  • Irene M. Gamba
  • Affiliation: Department of Mathematics and ICES, University of Texas at Austin, Austin, Texas 78712
  • MR Author ID: 241132
  • Email:
  • Jennifer Proft
  • Affiliation: ICES, University of Texas at Austin, Austin, Texas 78712
  • Email:
  • Received by editor(s): July 23, 2010
  • Received by editor(s) in revised form: October 27, 2010
  • Published electronically: June 15, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 153-190
  • MSC (2010): Primary 65M60, 76P05, 74S05
  • DOI:
  • MathSciNet review: 2833491