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Zbl 1214.30026
Olver, Sheehan
Numerical solution of Riemann-Hilbert problems: Painlevé II. (English)
[J] Found. Comput. Math. 11, No. 2, 153-179, erratum 181 (2011). ISSN 1615-3375; ISSN 1615-3383/e

Summary: We describe a new, spectrally accurate method for solving matrix-valued Riemann-Hilbert problems numerically. The effectiveness of this approach is demonstrated by computing solutions to the homogeneous Painlevé II equation. This can be used to relate initial conditions with asymptotic behavior.
MSC 2000:
*30E25 Boundary value problems, complex analysis
33E17 Painlevé-type functions
65E05 Numerical methods in complex analysis

Keywords: Riemann-Hilbert problems; spectral methods; collocation methods; Painlevé transcendents

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