General linear methods

Not to be confused with general linear models or generalized linear models.

General linear methods (GLMs) are a large class of numerical methods used to obtain numerical solutions to ordinary differential equations. They include multistage Runge–Kutta methods that use intermediate collocation points, as well as linear multistep methods that save a finite time history of the solution. John C. Butcher originally coined this term for these methods and has written a series of review papers,[1][2][3] a book chapter,[4] and a textbook[5] on the topic. His collaborator, Zdzislaw Jackiewicz also has an extensive textbook[6] on the topic. The original class of methods were originally proposed by Butcher (1965), Gear (1965) and Gragg and Stetter (1964).

  1. ^ Butcher, John C. (February–March 1996). "General linear methods". Computers & Mathematics with Applications. 31 (4–5): 105–112. doi:10.1016/0898-1221(95)00222-7.
  2. ^ Butcher, John (May 2006). "General linear methods". Acta Numerica. 15: 157–256. Bibcode:2006AcNum..15..157B. doi:10.1017/S0962492906220014. S2CID 125962375.
  3. ^ Butcher, John (February 2009). "General linear methods for ordinary differential equations". Mathematics and Computers in Simulation. 79 (6): 1834–1845. doi:10.1016/j.matcom.2007.02.006.
  4. ^ Butcher, John (2005). "General Linear Methods". Numerical Methods for Ordinary Differential Equations. John Wiley & Sons, Ltd. pp. 357–413. doi:10.1002/0470868279.ch5. ISBN 9780470868270. S2CID 2334002.
  5. ^ Butcher, John (1987). The numerical analysis of ordinary differential equations: Runge–Kutta and general linear methods. Wiley-Interscience. ISBN 978-0-471-91046-6.
  6. ^ Jackiewicz, Zdzislaw (2009). General Linear Methods for Ordinary Differential Equations. Wiley. ISBN 978-0-470-40855-1.