RiemannHilbert Problems, their Numerical Solution, and the Computation of Nonlinear Special Functions

RiemannHilbert 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 RiemannHilbert problem. This book provides introductions to both computational complex analysis, as well as to the applied theory of RiemannHilbert problems from an analytical and numerical perspective. Following a full-discussion of applications to integrable systems, differential equations and special function theory, the authors include six fundamental examples and five more sophisticated examples of the analytical and numerical RiemannHilbert method, each of mathematical or physical significance, or both. As the most comprehensive book to date on the applied and computational theory of RiemannHilbert problems, this book is ideal for graduate students and researchers interested in a computational or analytical introduction to the RiemannHilbert method.