Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions

Häftad, Engelska, 2015

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Beskrivning

Riemann–Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann–Hilbert problem. This book, the most comprehensive one to date on the applied and computational theory of Riemann-Hilbert problems, includes:An introduction to computational complex analysis.An introduction to the applied theory of Riemann–Hilbert problems from an analytical and numerical perspective.A discussion of applications to integrable systems, differential equations, and special function theory.Six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann–Hilbert method, each of mathematical or physical significance or both.

Produktinformation

Utgivningsdatum:2015-12-30
Mått:152 x 229 x 27 mm
Vikt:835 g
Format:Häftad
Språk:Engelska
Antal sidor:391
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9781611974195

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik

Mer om författaren

Thomas Trogdon is an NSF Postdoctoral Fellow at the Courant Institute of Mathematical Sciences, New York University. He was awarded the 2014 SIAM Richard C. DiPrima Prize for his dissertation, which shares its title with this book. He has published in the fields of numerical analysis, approximation theory, optical physics, integrable systems, partial differential equations and random matrix theory. Sheehan Olver is a Senior Lecturer in the School of Mathematics and Statistics at the University of Sydney. Dr Olver was awarded the 2012 Adams Prize for his work on the numerical solution of Riemann–Hilbert problems. He has published in the fields of numerical analysis, approximation theory, integrable systems, oscillatory integrals, spectral methods and random matrix theory.

Innehållsförteckning

Chapter 1: Classical Applications of Riemann–Hilbert ProblemsChapter 2: Riemann–Hilbert ProblemsChapter 3: Inverse Scattering and Nonlinear Steepest DescentChapter 4: Approximating FunctionsChapter 5: Numerical Computation of Cauchy TransformsChapter 6: The Numerical Solution of Riemann–Hilbert ProblemsChapter 7: Uniform Approximation Theory for Riemann–Hilbert ProblemsChapter 8: The Korteweg–de Vries and Modified Korteweg–de Vries EquationsChapter 9: The Focusing and Defocusing Nonlinear Schrödinger EquationsChapter 10: The Painlevé II TranscendentsChapter 11: The Finite-Genus Solutions of the Korteweg–de Vries EquationChapter 12: The Dressing Method and Nonlinear SuperpositionAppendix A: Function Spaces and Functional AnalysisAppendix B: Fourier and Chebyshev SeriesAppendix C: Complex AnalysisAppendix D: Rational ApproximationAppendix E: Additional KdV Results.