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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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A review of numerical methods for nonlinear partial differential equations
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by Eitan Tadmor PDF
Bull. Amer. Math. Soc. 49 (2012), 507-554 Request permission


Numerical methods were first put into use as an effective tool for solving partial differential equations (PDEs) by John von Neumann in the mid-1940s. In a 1949 letter von Neumann wrote “the entire computing machine is merely one component of a greater whole, namely, of the unity formed by the computing machine, the mathematical problems that go with it, and the type of planning which is called by both.” The “greater whole” is viewed today as scientific computation: over the past sixty years, scientific computation has emerged as the most versatile tool to complement theory and experiments, and numerical methods for solving PDEs are at the heart of many of today’s advanced scientific computations. Numerical solutions found their way from financial models on Wall Street to traffic models on Main Street. Here we provide a bird’s eye view on the development of these numerical methods with a particular emphasis on nonlinear PDEs.
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Additional Information
  • Eitan Tadmor
  • Affiliation: Department of Mathematics and Institute for Physical Science & Technology, Center of Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, Maryland 20742
  • MR Author ID: 170110
  • ORCID: 0000-0001-7424-6327
  • Email:
  • Received by editor(s): March 9, 2011
  • Received by editor(s) in revised form: May 27, 2012
  • Published electronically: July 20, 2012

  • Dedicated: To Heinz-Otto Kreiss with friendship and appreciation
  • © Copyright 2012 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 49 (2012), 507-554
  • MSC (2010): Primary 35J60, 35K55, 35L65, 35L70, 65Mxx, 65Nxx
  • DOI:
  • MathSciNet review: 2958929