Displaying similar documents to “Analysis of the accuracy and convergence of equation-free projection to a slow manifold”

Gradient descent and fast artificial time integration

Uri M. Ascher, Kees van den Doel, Hui Huang, Benar F. Svaiter (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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The integration to steady state of many initial value ODEs and PDEs using the forward Euler method can alternatively be considered as gradient descent for an associated minimization problem. Greedy algorithms such as steepest descent for determining the step size are as slow to reach steady state as is forward Euler integration with the best uniform step size. But other, much faster methods using bolder step size selection exist. Various alternatives are investigated from both theoretical...

Experiments with Krylov subspace methods on a massively parallel computer

Martin Hanke, Marlis Hochbruck, Wilhelm Niethammer (1993)

Applications of Mathematics

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In this note, we compare some Krylov subspace iterative methods on the MASPAR, a massively parallel computer with 16K processors. In particular, we apply these methods to solve large sparse nonsymmetric linear systems arising from elliptic partial differential equations. The methods under consideration include conjugate gradient type methods, semiiterative methods, and a hybrid variant. Our numerical results show that, on the MASPAR, one should compare iterative methods rather on the...

On consistency, stability and convergence of staggered solution procedures

Ewa Turska, Bernardo A. Schrefler (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The simultaneous and staggered procedures of solving a partitioned form of a coupled system of ordinary differential equations are presented. Formulas for errors are compared. Counter-examples for convergence with a constant number of iterations at each time step are given.