Some secant approximations for Rosenbrock W-methods

Authors:
Paolo Novati
Affiliations:
Dipartimento di Matematica Pura ed Applicata, Unversità dell'Aquila, Via Vetoio, Coppito, 67010 L'Aquila, Italy
Venue:
Applied Numerical Mathematics
Year:
2008

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High-order W-methods

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Abstract

Here we present a class of W-methods for stiff ODEs based on some special approximations of the Jacobian matrices that allow to reduce the number of order conditions. The approximations are considered modifications of some rank-1 updates, known from quasi-Newton methods. Two new embedded W-methods of order 3 and 4 are constructed and tested on some classical stiff equations arising from the semidiscretization of parabolic problems.