Numerical Solution of Riemann–Hilbert Problems: Painlevé II

被引：0

作者：

Sheehan Olver

机构：

[1] Oxford University Mathematical Institute,

来源：

Foundations of Computational Mathematics | 2011年 / 11卷

关键词：

Riemann–Hilbert problems; Spectral methods; Collocation methods; Painlevé transcendents; 30E25; 33E17; 65E05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：153 / 179

页数：26

共 50 条

[1] Numerical Solution of Riemann-Hilbert Problems: Painlev, II
Olver, Sheehan
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2011, 11 (02) : 153 - 179
[2] Erratum to: Numerical Solution of Riemann–Hilbert Problems: Painlevé II
Sheehan Olver
Foundations of Computational Mathematics, 2011, 11 (2) : 181 - 181
[3] Automatic Deformation of Riemann–Hilbert Problems with Applications to the Painlevé II Transcendents
Georg Wechslberger
Folkmar Bornemann
Constructive Approximation, 2014, 39 : 151 - 171
[4] Automatic Deformation of Riemann-Hilbert Problems with Applications to the Painlev, II Transcendents
Wechslberger, Georg
Bornemann, Folkmar
CONSTRUCTIVE APPROXIMATION, 2014, 39 (01) : 151 - 171
[5] A Riemann—Hilbert approach to Painlevé IV
Marius van der Put
Jaap Top
Journal of Nonlinear Mathematical Physics, 2013, 20 : 165 - 177
[6] Nonlinear Steepest Descent and Numerical Solution of Riemann-Hilbert Problems
Olver, Sheehan
Trogdon, Thomas
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2014, 67 (08) : 1353 - 1389
[7] Numerical solution of scattering problems using a Riemann-Hilbert formulation
Llewellyn Smith, Stefan Gregory
Luca, Elena
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2019, 475 (2229):
[8] Numerical Solution of Riemann–Hilbert Problems: Random Matrix Theory and Orthogonal Polynomials
Sheehan Olver
Thomas Trogdon
Constructive Approximation, 2014, 39 : 101 - 149
[9] Numerical Solution of the Riemann-Hilbert Problem
Nasser, Mohamed M. S.
PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2008, 40 : 9 - 29
[10] Numerical Solution of Riemann-Hilbert Problems: Random Matrix Theory and Orthogonal Polynomials
Olver, Sheehan
Trogdon, Thomas
CONSTRUCTIVE APPROXIMATION, 2014, 39 (01) : 101 - 149

← 1 2 3 4 5 →