Current Challenges in Stability Issues for Numerical Differential Equations: Cetraro, Italy 2011, Editors: Luca Dieci, Nicola Guglielmi

✍ Scribed by Wolf-Jürgen Beyn, Luca Dieci, Nicola Guglielmi, Ernst Hairer, Jesús María Sanz-Serna, Marino Zennaro (auth.)

Publisher: Springer International Publishing
Year: 2014
Tongue: English
Leaves: 324
Series: Lecture Notes in Mathematics 2082 C.I.M.E. Foundation Subseries
Edition: 1
Category: Library

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✦ Synopsis

This volume addresses some of the research areas in the general field of stability studies for differential equations, with emphasis on issues of concern for numerical studies.

Topics considered include: (i) the long time integration of Hamiltonian Ordinary DEs and highly oscillatory systems, (ii) connection between stochastic DEs and geometric integration using the Markov chain Monte Carlo method, (iii) computation of dynamic patterns in evolutionary partial DEs, (iv) decomposition of matrices depending on parameters and localization of singularities, and (v) uniform stability analysis for time dependent linear initial value problems of ODEs.

The problems considered in this volume are of interest to people working on numerical as well as qualitative aspects of differential equations, and it will serve both as a reference and as an entry point into further research.

✦ Table of Contents

Front Matter....Pages i-ix
Long-Term Stability of Symmetric Partitioned Linear Multistep Methods....Pages 1-37
Markov Chain Monte Carlo and Numerical Differential Equations....Pages 39-88
Stability and Computation of Dynamic Patterns in PDEs....Pages 89-172
Continuous Decompositions and Coalescing Eigenvalues for Matrices Depending on Parameters....Pages 173-264
Stability of Linear Problems: Joint Spectral Radius of Sets of Matrices....Pages 265-313
Back Matter....Pages 315-316

✦ Subjects

Computational Mathematics and Numerical Analysis; Applications of Mathematics; Ordinary Differential Equations; Partial Differential Equations; Algorithms; Linear and Multilinear Algebras, Matrix Theory

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