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Error propagation of general linear methods for ordinary differential equations |
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| Authors: | JC Butcher Z Jackiewicz WM Wright |
| Institution: | aDepartment of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand;bDepartment of Mathematics, Arizona State University, Tempe, Arizona 85287, USA;cDepartment of Mathematical and Statistical Sciences, La Trobe University, Melbourne, Vic. 3086, Australia |
| Abstract: | We discuss error propagation for general linear methods for ordinary differential equations up to terms of order p+2, where p is the order of the method. These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p+1. The results of numerical experiments confirm the reliability of these estimates. This research has applications in the design of robust stepsize and order changing strategies for algorithms based on general linear methods. |
| Keywords: | General linear methods Nordsieck representation Error propagation Local error estimation for methods of adjacent orders Adaptive stepsize selection Stability analysis |
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