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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


Peter Philip
LMU Munich
MR ID: 639375
Reference #


Posted date
2022-10-31 06:24:54
Revised date
2022-10-31 06:24:54
Notes type
   Standard Course Offering
   Differential Equations
      Ordinary Differential Equations
   Numerical Analysis

Numerical Mathematics II: Numerical Solution of Ordinary Differential Equations

We study explicit and implicit methods for initial value problems.
For general Runge-Kutta methods, Butcher's theory of rooted trees
is presented in detail, proving Butcher's theorem on conditions for high orders of consistency and convergence. Further topics include
collocation methods, stability theory, stiff equations, asymptotic error expansions, extrapolation methods, and stepsize control.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v1 PDF (1.1M) 10/31/22