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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.


A second-order numerical method for the aggregation equations
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by José A. Carrillo, Ulrik S. Fjordholm and Susanne Solem HTML | PDF
Math. Comp. 90 (2021), 103-139 Request permission


Inspired by so-called TVD limiter-based second-order schemes for hyperbolic conservation laws, we develop a formally second-order accurate numerical method for multi-dimensional aggregation equations. The method allows for simulations to be continued after the first blow-up time of the solution. In the case of symmetric, $\lambda$-convex potentials with a possible Lipschitz singularity at the origin, we prove that the method converges in the Monge–Kantorovich distance towards the unique gradient flow solution. Several numerical experiments are presented to validate the second-order convergence rate and to explore the performance of the scheme.
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Additional Information
  • José A. Carrillo
  • Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
  • ORCID: 0000-0001-8819-4660
  • Email:
  • Ulrik S. Fjordholm
  • Affiliation: Department of Mathematics, University of Oslo, 0851 Oslo, Norway
  • MR Author ID: 887509
  • ORCID: 0000-0001-8528-5786
  • Email:
  • Susanne Solem
  • Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
  • MR Author ID: 1106760
  • Email:
  • Received by editor(s): November 19, 2019
  • Received by editor(s) in revised form: April 22, 2020
  • Published electronically: August 18, 2020
  • Additional Notes: The first author was partially supported by the EPSRC grant number EP/P031587/1 and the Advanced Grant Nonlocal-CPD (Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization) of the European Research Council Executive Agency (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 883363).
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 103-139
  • MSC (2010): Primary 35R09, 35D30, 35Q92, 65M12, 65M08
  • DOI:
  • MathSciNet review: 4166455