Abstract
We consider ROW-methods for stiff initial value problems, where the stage equations are solved by Krylov techniques. By using a certain ‘multiple Arnoldi process’ over all stages the order of the fully-implicit one-step scheme can be preserved with low Krylov dimensions. Explicit estimates for minimal order preserving dimensions are derived. They depend on the parameters of the method only, not on the dimension of the ODE. Stability restrictions usually require larger dimensions, of course, but this can be done adaptively. These results justify to adopt the step size control of the underlying ROW-method. The widely used ROW-methods of order 4 are discussed in detail and numerical illustrations are given. For the special class of semilinear systems with stiffness in a constant linear part we establish the order 2 of B-consistency for these Krylov-W-methods.
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This work was supported by the Deutsche Forschungsgemeinschaft.
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Weiner, R., Schmitt, B.A. Order results for Krylov-W-methods. Computing 61, 69–89 (1998). https://doi.org/10.1007/BF02684451
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DOI: https://doi.org/10.1007/BF02684451