Collected Lectures On The Preservation Of Stability Under Discretization (proceedings In Applied Mathematics)
by Donald Estep /
1987 / English / DjVu
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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.
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.
