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Padé Methods for Painlevé Equations

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 42)

DOI: 10.1007/978-981-16-2998-3

ISBN: 978-981-16-2997-6

Publisher: Springer Singapore - Springer Journals

Sep 2, 2021

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Chapter 1Padé Approximation and Differential Equation

Nagao, Hidehtio; Yamada, Yasuhiko

Pages: 1 –8

[The Padé approximation gives rational functions P(x)Q(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Chapter 2Padé Approximation for PVI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_\mathrm{VI}$$\end{document}

Nagao, Hidehtio; Yamada, Yasuhiko

Pages: 9 –30

[We will consider the Padé approximation problem associated with the function ψ(x)=(1-x)α(1-xt)β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
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Chapter 3Padé Approximation for q-Painlevé/Garnier Equations

Nagao, Hidehtio; Yamada, Yasuhiko

Pages: 31 –47

[In this chapter, we consider the Padé approximation where the function ψ(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Chapter 4Padé Interpolation

Nagao, Hidehtio; Yamada, Yasuhiko

Pages: 49 –59

[The Padé approximation has a discrete analog: the Padé interpolation. In fact, the latter was known before the former. We study the discrete Painlevé equations using the Padé interpolation. In this chapter, we consider the interpolation on a q-grid defined by...
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Chapter 5Padé Interpolation on q-Quadratic Grid

Nagao, Hidehtio; Yamada, Yasuhiko

Pages: 61 –73

[In the Padé interpolation, one can make various choices for the grid (interpolating points: x0,x1,x2,⋯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
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Chapter 6Multicomponent Generalizations

Nagao, Hidehtio; Yamada, Yasuhiko

Pages: 75 –83

[We will discuss generalizations of isomonodromic deformations to higher order or higher rank, using the multicomponent Padé approximations. Two kinds of approximation/interpolation problems and their duality relations play an important role.]

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