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A general framework for solving Riemann–Hilbert problems numerically

Sheehan Olver
Journal / Anthology

Numerische Mathematik
Year: 2012
Volume: 122
Page range: 305–340

A new, numerical framework for the approximation of solutions to matrix valued Riemann–Hilbert problems is developed, based on a recent method for the homogeneous Painlevé II Riemann–Hilbert problem. We demonstrate its effectiveness by computing solutions to other Painlevé transcendents. An implementation in Mathematica is made available online.