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Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods. By introducing a sui ...
We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerica ...
B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elegant derivation of order conditions, and a substitution law gives much insight i ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
Shape Optimization problems governed by partial differential equations result from many applications in computational fluid dynamics; they involve the repetitive evaluation of outputs expressed as functionals of the field variables and usually imply big co ...
The theory of discrete variational mechanics has its roots in the optimal control literature of the 1960's. The past ten years have seen a major development of discrete variational mechanics and corresponding numerical integrators, due largely to pioneerin ...
In the absence of a full analytical treatment of nonlinear structure formation in the universe, numerical simulations provide the critical link between the properties of the underlying model and the features of the observed structures. Currently N-body sim ...
We consider the long time behavior of the semidiscrete scheme for the Perona-Malik equation in one dimension. We prove that approximated solutions converge, in a slow time scale, to solutions of a limit problem. This limit problem evolves piecewise constan ...
A direct integration algorithm, based on double exponential-type quadrature rules, is presented for the efficient computation of the Sommerfeld integral tails, arising in the evaluation of multilayered Green's functions. The proposed scheme maintains the e ...
Institute of Electrical and Electronics Engineers2011
In this report we study and compare particular integration methods to solve ordinary differential equations, which are separable in solvable parts. The main source for this work is the article of Blanes and Casas: "On the necessity of negative coefficient ...