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Numerical solution of Riemann-Hilbert problems: Painlevé II. (English) Zbl 1214.30026
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:
30E25Boundary value problems, complex analysis
33E17Painlevé-type functions
65E05Numerical methods in complex analysis
References:
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