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Stabilized starting algorithms for collocation Runge-Kutta methods

✍ Scribed by S. González-Pinto; J.I. Montijano; S. Pérez-Rodríguez

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
861 KB
Volume
45
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper, we propose a technique to stabilize some starting algorithms often used in the Newton-type iterations appearing when collocation Runge-Kutta methods are applied to solve stiff initial value problems. By following the ideas given in [1], we analyze the order (classical and stiff) • of the new starting algorithms and pay special attention to their error amplifying functions. Prom the computational point of view, the new algorithms require the solution of an additional linear system per integration step, but as shown in the numerical experiments, this extra cost is compensated in most of the problems by their better stability properties.

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Multi-Symplectic Runge–Kutta Collocation
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A number of conservative PDEs, like various wave equations, allow for a multisymplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numer