Current Challenges in Stability Issues for Numerical Differential Equations [electronic resource] : Cetraro, Italy 2011, Editors: Luca Dieci, Nicola Guglielmi / by Wolf-Jürgen Beyn, Luca Dieci, Nicola Guglielmi, Ernst Hairer, Jesús María Sanz-Serna, Marino Zennaro.
By: Beyn, Wolf-Jürgen [author.].
Contributor(s): Dieci, Luca [author.] | Guglielmi, Nicola [author.] | Hairer, Ernst [author.] | Sanz-Serna, Jesús María [author.] | Zennaro, Marino [author.] | SpringerLink (Online service).
Material type:
BookSeries: Lecture Notes in Mathematics: 2082Publisher: Cham : Springer International Publishing : Imprint: Springer, 2014Description: IX, 313 p. 121 illus., 105 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319013008.Subject(s): Mathematics | Matrix theory | Differential Equations | Differential equations, partial | Computer science -- Mathematics | Algorithms | Mathematics | Computational Mathematics and Numerical Analysis | Applications of Mathematics | Ordinary Differential Equations | Partial Differential Equations | Algorithms | Linear and Multilinear Algebras, Matrix TheoryDDC classification: 518 | 518 Online resources: Click here to access online Studies on current challenges in stability issues for numerical differential equations -- Long-Term Stability of Symmetric Partitioned Linear Multistep Methods -- Markov Chain Monte Carlo and Numerical Differential Equations -- Stability and Computation of Dynamic Patterns in PDEs -- Continuous Decompositions and Coalescing Eigen values for Matrices Depending on Parameters -- Stability of linear problems: joint spectral radius of sets of matrices.
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.
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