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Extrapolated multistep methods and local-global step size control

Kulikov, Gennady Yu; Shindin, S.K.

Lecture Notes in Computer Science, 2657 (2003), 540-549

In recent papers [7], [8], [9], [11] the technique for a local and global errors estimation and the local-global step size control were presented to solve both ordinary differential equations and semi-explicit index 1 differential-algebraic systems by multistep methods with any reasonable accuracy obtained automatically. Now we extend those results to the concept of multistep extrapolation and demonstrate on numerical examples how such methods work in practice.