Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods
KAUST Grant NumberFIC/2010/05
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Abstract© 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
CitationMozartova A, Savostianov I, Hundsdorfer W (2015) Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods. Journal of Computational and Applied Mathematics 279: 159–172. Available: http://dx.doi.org/10.1016/j.cam.2014.10.025.
SponsorsThe work of A. Mozartova has been supported by a grant from the Netherlands Organization for Scientific Research NWO. The work of I. Savostianov and W. Hundsdorfer for this publication has been supported by Award No. FIC/2010/05 from the King Abdullah University of Science and Technology (KAUST).