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

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Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions is written by Thomas Trogdon and published by SIAM. It's available with International Standard Book Number or ISBN identification 1611974208 (ISBN 10) and 9781611974201 (ISBN 13).

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, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.