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The code automatically detects and locates accurately the switching points of the PWS, ... Keywords: Nonsmooth initial value problems, Filippov systems, detection of discontinuities, adaptive Runge-Kutta methods 2 September 2015 Journal of Scientific Computing: Volume 64 Issue 3, September 2015 Publisher: Plenum Press Bibliometrics: Citation Count: 0 In this paper we study functionally fitted methods based on explicit two step peer formulas. We show that with $$s$$s stages it is possible to get explicit fitted methods for fitting spaces of high dimension $$2s$$2s, by proving the existence and uniqueness of such formulas. Then, we obtain particular methods ... Keywords: 65L99, Peer methods, 65L07, 65L05, Periodic problems, Exponential fitting 3 February 2015 Advances in Computational Mathematics: Volume 41 Issue 1, February 2015 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 In this paper new one-step methods that combine Runge---Kutta (RK) formulae with a suitable projection after the step are proposed for the numerical solution of Initial Value Problems. The aim of this projection is to preserve some first integral in the numerical integration. In contrast with standard orthogonal projection, the ... Keywords: 65L06, Dispersion error, Numerical geometric integration, 65L05, Initial value problems, Projection methods, Explicit Runge---Kutta methods 4 October 2012 Journal of Computational and Applied Mathematics: Volume 236 Issue 16, October, 2012 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 3 We present and analyze energy-conserving methods for the numerical integration of IVPs of Poisson type that are able to preserve some Casimirs. Their derivation and analysis is done following the ideas of Hamiltonian BVMs (HBVMs) (see Brugnano et al. [10] and references therein). It is seen that the proposed approach ... Keywords: 65P10, Energy-preserving methods, Hamiltonian boundary value methods, Line integral methods, One-step methods, Ordinary differential equations, Poisson problems, 65L05 5 September 2012 Journal of Computational and Applied Mathematics: Volume 236 Issue 15, September, 2012 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 1 In this paper, explicit Runge-Kutta (RK) schemes with minimum storage requirements for systems with very large dimension that arise in the spatial discretization of some partial differential equations are considered. A complete study of all four stage fourth-order schemes of the minimum storage families of Williamson (1980) 2], van der ... Keywords: Initial value problems, Low storage implementations, Runge-Kutta schemes 6 October 2011 Applied Numerical Mathematics: Volume 61 Issue 10, October, 2011 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 4 The stroboscopic averaging method (SAM) is a technique for the integration of highly oscillatory differential systems dy/dt=f(y,t) with a single high frequency. The method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averaging which constructs an averaged differential system dY/dt=F(Y) whose solutions Y ... Keywords: Multirevolution methods, Stroboscopic averaging, Differential algebraic equations, Highly oscillatory problems 7 August 2011 Mathematics and Computers in Simulation: Volume 81 Issue 12, August, 2011 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 3 This paper is concerned with the long term behaviour of the error generated by one step methods in the numerical integration of periodic flows. Assuming numerical methods where the global error possesses an asymptotic expansion and a periodic flow with the period depending smoothly on the starting point, some conditions ... Keywords: Invariant preservation, Runge-Kutta methods, Geometric integration, Long-time integration 8 April 2011 Applied Numerical Mathematics: Volume 61 Issue 4, April, 2011 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 1 The so-called two-step peer methods for the numerical solution of Initial Value Problems (IVP) in differential systems were introduced by R. Weiner, B.A. Schmitt and coworkers as a tool to solve different types of IVPs either in sequential or parallel computers. These methods combine the advantages of Runge-Kutta (RK) and ... Keywords: Two-step methods, IVP, Peer methods, Stability 9 July 2010 SIAM Journal on Scientific Computing: Volume 32 Issue 4, June 2010 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 2 We are concerned with heterogeneous multiscale methods for the numerical integration of the equations of motion of mechanical systems subjected to fast vibrations. We suggest easily formulated asynchronous algorithms that bypass the need for explicitly determining the relations between macro- and microstates. The new algorithms have good geometric properties and ... Keywords: heterogeneous multiscale methods, constrained systems, oscillatory problems, mechanical systems 10 May 2006 Journal of Computational and Applied Mathematics: Volume 189 Issue 1-2, May, 2006 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 1 Symplectic Runge-Kutta (RK) methods for general Hamiltonian systems are implicit and an iterative scheme must be used to obtain the solution at each step. In this paper the classical order and the pseudo-symplecticity order [Pseudo-symplectic Runge-Kutta methods, BIT 38 (1998) 439-461] of the one step method that results after @s ... Keywords: 65L05, Pseudo-symplectic properties, Runge-Kutta-Gauss methods, Starting algorithms for stage equations, 65L06, General Hamiltonian systems 11 January 2006 Numerische Mathematik: Volume 102 Issue 3, January 2006 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 3 A class of explicit multistep exponential methods for abstract semilinear equations is introduced and analyzed. It is shown that the k -step method achieves order k , for appropriate starting values, which can be computed by auxiliary routines or by one strategy proposed in the paper. Together with some implementation ... Keywords: 65J15, 65M20, 65L05, 65M12 12 December 1990 Numerische Mathematik: Volume 57 Issue 1, December 1990 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 1 This paper contains bounds for the mesh-size ratios h j +1 / h j of nonequidistant grids such that any combination of the widely used backward differentiation formulas with orders l , 1� l � m , m =3,4,5, performs zerostable. Keywords: AMS(MOS): 65L05, CR: G. 1.7 13 May 1989 Numerische Mathematik: Volume 54 Issue 3, May 1989 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 1 Stability regions of �-methods for the linear delay differential test equations $$\begin{gathered} y'(t) = py(t) + qy(t - \tau ),t > 0, \hfill \\ y(t) = \varphi (t),t \in [ - \tau ,0], \hfill \\ \end{gathered}$$ where � is a positive constant, are presented. In the case that p and ... Keywords: AMS(MOS): 65L20, CR: G1.7