1,065 research outputs found
Strong Stability Preserving Two-Step Runge-Kutta Methods
We investigate the strong stability preserving (SSP) property of two-step Runge– Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple\ud
subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy, and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order WENO discretizations
Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems
We are interested in high-order linear multistep schemes for time
discretization of adjoint equations arising within optimal control problems.
First we consider optimal control problems for ordinary differential equations
and show loss of accuracy for Adams-Moulton and Adams-Bashford methods, whereas
BDF methods preserve high--order accuracy. Subsequently we extend these results
to semi--lagrangian discretizations of hyperbolic relaxation systems.
Computational results illustrate theoretical findings
Exponentially fitted fifth-order two-step peer explicit methods
The so called peer methods for the numerical solution of Initial Value Problems (IVP) in ordinary differential systems were introduced by R. Weiner et al [6, 7, 11, 12, 13] for solving different types of problems either in sequential or parallel computers. In this work, we study exponentially fitted three-stage peer schemes that are able to fit functional spaces with dimension six. Finally, some numerical experiments are presented to show the behaviour of the new peer schemes for some periodic problems
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