2 edition of **Algebraic analysis and the exact WKB analysis for systems of differential equations.** found in the catalog.

Algebraic analysis and the exact WKB analysis for systems of differential equations.

RIMS Workshop on Algebraic Analysis and the Exact WKB Analysis for Systems of Differential Equations (2006 Kyoto, Japan)

- 46 Want to read
- 30 Currently reading

Published
**2008**
by Research Institute for Mathematical Sciences, Kyoto University in Kyoto, Japan
.

Written in English

- Differential equations -- Congresses

**Edition Notes**

Genre | Congresses |

Series | RIMS kōkyūroku. Bessatsu -- B5 |

Contributions | Kyōto Daigaku. Sūri Kaiseki Kenkyūjo. |

Classifications | |
---|---|

LC Classifications | QA370 .R56 2006 |

The Physical Object | |

Pagination | vii, 280 p. : |

Number of Pages | 280 |

ID Numbers | |

Open Library | OL24078581M |

LC Control Number | 2009513118 |

In mathematics, an equation is a statement that asserts the equality of two word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English any equality is an equation.. Solving an equation containing variables consists of determining which values of the. Topics covered includes: State space analysis of differential-algebraic equations, Properly formulated DAEs with tractability index 2, The state space form, Index reduction via differentiation, Stability criteria for differential-algebraic systems, Asymptotic stability of .

Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic. this book is confusing, the chapters are not well explained. I don't advise to buy this book to study linear algebra or differential equations. The matlab examples are not self explanatory. It lacks of good examples and does not follow an order easy to follow for the reader. I give it the 2 stars because it was very s: 4.

Toward the exact WKB analysis of differential equations, linear or non-linear. Kyoto, Japan: Kyoto University Press, © (OCoLC) Named Person: Gregor Wentzel; Hendrik Anthony Kramers; Léon Brillouin: Document Type: Book: All Authors / Contributors: Christopher J Howls; Takahiro Kawai; Yoshitsugu Takei. The main approach used by the authors is the so-called WKB (Wentzel–Kramers–Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painlevé functions.

You might also like

The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text.

The book is addressed to graduate students and researchers in mathematics Cited by: Algebraic Analysis of Differential Equations Virtual turning points — A gift of microlocal analysis to the exact WKB analysis.

Pages Book Title Algebraic Analysis of Differential Equations Book Subtitle from Microlocal Analysis to Exponential Asymptotics Editors. Algebraic Analysis of Differential Equations The work of T. Kawai on exact WKB analysis Yoshitsugu Takei [21] On the boundary value problem for the elliptic system of linear diﬀerential equations, S´em.

Goulaouic-Schwartz, –,Expos´e 19,(with M. In mathematics, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a systems occur as the general form of (systems of) differential equations for vector–valued functions x in one independent variable t, (˙ (), (),) =where: [,] → is a vector of.

analysis, Part 1 — Microlocal analysis and differential equations Nobuyuki Tose 11 The work of T. Kawai on hyperfunction theory and microlocal analysis, Part 2 — Operators of infinite order and convolution equations Takashi Aoki 15 The work of T.

Kawai on exact WKB analysis Yoshitsugu Takei 19 Part II Contributed papers. Publisher Summary. This chapter discusses the solvable models in statistical mechanics and Riemann surfaces of genus greater than one.

Most recently, it was discovered that there is an N-state generalization of the Ising model which seems to possess all of its nice model is the chiral Potts model or Z N symmetric model. A most natural place to commence the investigation of any.

Algebraic Analysis of Singular Perturbation Theory Takahiro Kawai, Yoshitsugu Takei The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter.

WKB analysis and Stokes geometry of differential equations Dunkl theory, special functions sub-Riemannian geometry and sub-elliptic operators holonomic systems ODEs in the complex plane holomorphic vector fields, normal forms summability of formal solutions of difference equations integrable systems with applications to mathematical physics formal solutions of PDEs Gevrey.

Nonlinear Wave Equations and Fuchsian Equations 3 We shall construct singular solutions to the nonlinear wave equation () u_{tt}-\triangle u=f(t, x;\partial_{t}u, \nabla u), where \nabla is the gradient with respect to x.

It helps to consider an elementary ordinary differential equation u''=(u')^{2} which has a solution u=-\log t It suggests that () has a singular solution led by a.

Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful.

m (m =1,2,3,), is written down as a system of the ﬁrst order nonlinear ordinary diﬀerential equations. One of the advantages of the new expressionis thatitis more suitedforWKB analysis; forexample the discussiongivenin [KoNT] on the description of the Stokes geometry of (PIV) m.

And in, the instanton corrections to the prepotential of N = 2 SU(2) SYM has been computed by using the exact WKB analysis. The quantum SW curve for N = 2 gauge theories have been studied in. The purpose of the present paper is to derive the TBA equations for the exact WKB periods of the Mathieu equation in the weak coupling region.

Differential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others.

This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and Reviews: 1.

A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system.÷Ordinary Differential Equations and Linear Algebra: A Systems Approach÷systematically develops the linear algebra needed to solve systems of ODEs and includes over.

Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials.

In recent years, there have been a few works about the numerical method of the fractional differential-algebraic equations. Nonlinear Wave Equations and Fuchsian Equations 3 We shall construct singular solutions to the nonlinear wave equation () u tt −Δu = f(t,x;∂ tu,∇u), where ∇ is the gradient with respect to x.

It helps to consider an elementary ordinary diﬀerential equation u =(u)2,which has a solution u = − suggests that () has a singular solution led by a. This diagram has two ends, and the corresponding differential equations play an important role in exact WKB analysis: The Airy equation is used as a canonical equation to derive the connection.

The first chapter is a brief, but a sufficiently comprehensive introduction to the methods of Lie group analysis of ordinary and partial differential equations. Heun s Differential Equation and WKB Analysis 65 we recover the Treibich s result [21].

Gesztesy and Weikard [8] developed a theory of Picard s potential, and it would be related to our one. We introduce a proposition which plays a crucial role of proving Theorem Observe that a product of two solutions to () (-\displaystyle \frac{d^{2}}{dx^{2}}+v(x)) fx)=Ef(x) satisfies ( _____: On the exact WKB analysis for the third order ordinary differential equations with a large parameter, Asian J.

Math., 2 (), – zbMATH MathSciNet Google Scholar [AKT3] _____: On the exact steepest descent method: A new method for the description of Stokes curves, J. Math. Phys., 42 (), – zbMATH CrossRef.

12 pages, An extended version of talk given at "Algebraic Analysis and the Exact WKB Analysis for Systems of Differential Equations", RIMS, Kyoto, December Subjects: Classical Analysis and ODEs (); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems () MSC classes: 34M35,33E10,34E Cite as.Heun’s Differential Equation and WKB Analysis 63 §2.

Finite-Gap Potential We recall deﬁnitions of the ﬁnite-gap potential and the algebro-geometric ﬁnite-gap potential. Deﬁnition Let q(x) be a periodic, smooth, real function, H the operator −d 2/dx +q(x), and the set σ b(H) deﬁned as follows: () E ∈ σ.Linear Algebra C Quadratic equations in two or three variables by Leif Mejlbro - BookBoon The book is a collection of solved problems in linear algebra, this fourth volume covers quadratic equations in two or three variables.

All examples are solved, and the solutions usually consist of .