Collected Lectures on the Preservation of Stability Under Discretization

Stability in differential equations concerns the global effects of local perturbations. Many students of differential equaltions first learn about stability in the form of well-posedness and the classic Lax equivalence theorem (that well-posedness plus consistency equals convergence). However, many other notions of stability are equally important in practice, and this volume tackles the challenging concepts of stability beyond well-posedness. The lectures in this volume were chosen to strike a reasonable balance between dynamical and classical analysis, between structure-preserving and character-preserving numerics, and between the preservation of stability under discretization and the study of stability by computation. The broad range of topics presented in this book exposes many parallel themes. Armed with an understanding of the broader picture and in possession of a good set of references, the reader should then be prepared to seek a deeper comprehension of stability.