The Mathematical Institute, University of Oxford, Eprints Archive

A general framework for solving Riemann-Hilbert problems
numerically

Olver, Sheehan (2010) A general framework for solving Riemann-Hilbert problems
numerically.
Technical Report. Unspecified. (Submitted)

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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 Painlev\'e II Riemann- Hilbert problem. We demonstrate its effectiveness by computing solutions to other Painlev\'e transcendents.

An implementation in MATHEMATICA is made available online.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Partial differential equations
H - N > Integral equations
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:938
Deposited By:Lotti Ekert
Deposited On:24 Jul 2010 08:20
Last Modified:24 Jul 2010 08:20

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