東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Linked to FindBook

Google Book

Amazon

博客來

Numerical methods for metric graphs = Eigenvalue problems and parabolic partial differential equations /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical methods for metric graphs/ by Anna Weller.
Reminder of title:	Eigenvalue problems and parabolic partial differential equations /
Author:	Weller, Anna.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xxi, 190 p. :ill., digital ;24 cm.
[NT 15003449]:	Chapter 1. Introduction -- Chapter 2. Background: Graphs and Differential Equations -- Chapter 3. Finite Element Method -- Chapter 4. Spectral Solution Method -- Chapter 5. Computation of Quantum Graph Spectra -- Chapter 6. Numerical Results -- Chapter 7. Comparison of Finite Element and Spectral Galerkin Method -- Chapter 8. Application to the Simulation of Tau Propagation in Alzheimer's Disease -- Chapter 9. Conclusion.
Contained By:	Springer Nature eBook
Subject:	Graphic methods. -
Online resource:	https://doi.org/10.1007/978-3-032-05011-3
ISBN:	9783032050113

Numerical methods for metric graphs = Eigenvalue problems and parabolic partial differential equations /
Weller, Anna.

Numerical methods for metric graphsEigenvalue problems and parabolic partial differential equations /[electronic resource] :by Anna Weller. - Cham :Springer Nature Switzerland :2025. - xxi, 190 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23821617-9692 ;. - Lecture notes in mathematics ;v. 2382..

Chapter 1. Introduction -- Chapter 2. Background: Graphs and Differential Equations -- Chapter 3. Finite Element Method -- Chapter 4. Spectral Solution Method -- Chapter 5. Computation of Quantum Graph Spectra -- Chapter 6. Numerical Results -- Chapter 7. Comparison of Finite Element and Spectral Galerkin Method -- Chapter 8. Application to the Simulation of Tau Propagation in Alzheimer's Disease -- Chapter 9. Conclusion.

This book discusses the fundamentals of the numerics of parabolic partial differential equations posed on network structures interpreted as metric spaces. These so-called metric graphs frequently occur in the context of quantum graphs, where they are studied together with a differential operator and coupling conditions at the vertices. The two central methods covered here are a Galerkin discretization with linear finite elements and a spectral Galerkin discretization with basis functions obtained from an eigenvalue problem on the metric graph. The solution of the latter eigenvalue problems, i.e., the computation of quantum graph spectra, is therefore an important aspect of the method, and is treated in depth. Further, a real-world application of metric graphs to the modeling of the human connectome (brain network) is included as a major motivation for the investigated problems. Aimed at researchers and graduate students with a practical interest in diffusion-type and eigenvalue problems on metric graphs, the book is largely self-contained; it provides the relevant background on metric (and quantum) graphs as well as the discussed numerical methods. Numerous detailed numerical examples are given, supplemented by the publicly available Julia package MeGraPDE.jl.

ISBN: 9783032050113

Standard No.: 10.1007/978-3-032-05011-3doiSubjects--Topical Terms:

636683
Graphic methods.

LC Class. No.: QA90

Dewey Class. No.: 511.52

Numerical methods for metric graphs = Eigenvalue problems and parabolic partial differential equations /
LDR:02787nmm a22003375a 4500 001 2422365
003 DE-He213
005 20251121114916.0
006 m d
007 cr nn 008maaau
008 260505s2025 sz s 0 eng d
020 $a 9783032050113 $q (electronic bk.)
020 $a 9783032050106 $q (paper)
024 7 $a 10.1007/978-3-032-05011-3 $2 doi
035 $a 978-3-032-05011-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA90
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 511.52 $2 23
090 $a QA90 $b .W448 2025
100 1 $a Weller, Anna. $3 3804116
245 1 0 $a Numerical methods for metric graphs $h [electronic resource] : $b Eigenvalue problems and parabolic partial differential equations / $c by Anna Weller.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xxi, 190 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2382
505 0 $a Chapter 1. Introduction -- Chapter 2. Background: Graphs and Differential Equations -- Chapter 3. Finite Element Method -- Chapter 4. Spectral Solution Method -- Chapter 5. Computation of Quantum Graph Spectra -- Chapter 6. Numerical Results -- Chapter 7. Comparison of Finite Element and Spectral Galerkin Method -- Chapter 8. Application to the Simulation of Tau Propagation in Alzheimer's Disease -- Chapter 9. Conclusion.
520 $a This book discusses the fundamentals of the numerics of parabolic partial differential equations posed on network structures interpreted as metric spaces. These so-called metric graphs frequently occur in the context of quantum graphs, where they are studied together with a differential operator and coupling conditions at the vertices. The two central methods covered here are a Galerkin discretization with linear finite elements and a spectral Galerkin discretization with basis functions obtained from an eigenvalue problem on the metric graph. The solution of the latter eigenvalue problems, i.e., the computation of quantum graph spectra, is therefore an important aspect of the method, and is treated in depth. Further, a real-world application of metric graphs to the modeling of the human connectome (brain network) is included as a major motivation for the investigated problems. Aimed at researchers and graduate students with a practical interest in diffusion-type and eigenvalue problems on metric graphs, the book is largely self-contained; it provides the relevant background on metric (and quantum) graphs as well as the discussed numerical methods. Numerous detailed numerical examples are given, supplemented by the publicly available Julia package MeGraPDE.jl.
650 0 $a Graphic methods. $3 636683
650 0 $a Eigenvalues. $3 631789
650 0 $a Differential equations, Parabolic. $3 560916
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Numerical Analysis. $3 892626
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v. 2382. $3 3804117
856 4 0 $u https://doi.org/10.1007/978-3-032-05011-3
950 $a Mathematics and Statistics (SpringerNature-11649)