Current Challenges in Stability Issues for Numerical Differential Equations: Cetraro, Italy 2011, Editors: Luca Dieci, Nicola Guglielmi (Lecture Notes in Mathematics Book 2082)

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. Studies On Current Challenges In Stability Issues For Numerical Differential Equations / Luca Dieci, Nicola Guglielmi-- Long-term Stability Of Symmetric Partitioned Linear Multistep Methods / Paola Console And Ernst Hairer -- Markov Chain Monte Carlo And Numerical Differential Equations / J.m. Sanz-serna -- Stability And Computation Of Dynamic Patterns In Pdes / Wolf-jürgen Beyn, Denny Otten, And Jens Rottmann-matthes -- Continuous Decompositions And Coalescing Eigenvalues For Matrices Depending On Parameters / Luca Dieci ... [and 3 More] -- Stability Of Linear Problems: Joint Spectral Radius Of Sets Of Matrices / Nicola Guglielmi And Marino Zennaro. [with Contributions By] Wolf-jürgen Beyn [and 5 Others] ; Editors: Luca Dieci, Nicola Guglielmi. This Volume Is The Outgrowth Of Lectures Presented During The Cime-ems Summer School On Applied Mathematics ... Held In Cetraro (italy) In June 2011.--page V. Includes Bibliographical References (pages 311-313). 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