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A general framework for solving Riemann–Hilbert problems numerically

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Abstract

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.

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  1. School of Mathematics and Statistics, The University of Sydney, Sydney, Australia

    Sheehan Olver

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  1. Sheehan Olver
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Olver, S. A general framework for solving Riemann–Hilbert problems numerically. Numer. Math. 122, 305–340 (2012). https://doi.org/10.1007/s00211-012-0459-7

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  • DOI: https://doi.org/10.1007/s00211-012-0459-7

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