Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions - Trogdon, Thomas; Olver, Sheehan
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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: 1. An introduction to computational complex analysis. 2. An introduction to the applied theory of Riemann–Hilbert problems from an analytical and numerical perspective. 3. A discussion of applications to…mehr

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Produktbeschreibung
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: 1. An introduction to computational complex analysis. 2. An introduction to the applied theory of Riemann–Hilbert problems from an analytical and numerical perspective. 3. A discussion of applications to integrable systems, differential equations, and special function theory. 4. Six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann–Hilbert method, each of mathematical or physical significance or both.
Autorenporträt
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.