Engineering simulation and its applications: algorithms and numerical methods
Front Cover -- Engineering Simulation and its Applications -- Copyright -- Contents -- About the author -- Preface -- Acknowledgments -- 1 Introduction to engineering simulation -- 1.1 Introduction -- 1.2 What is a model? -- 1.3 Mathematical models -- 1.3.1 Algebraic equations -- 1.3.2 ODE models --...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Academic Press
2024
|
| Online-Zugang: | DE-706 Volltext |
| Zusammenfassung: | Front Cover -- Engineering Simulation and its Applications -- Copyright -- Contents -- About the author -- Preface -- Acknowledgments -- 1 Introduction to engineering simulation -- 1.1 Introduction -- 1.2 What is a model? -- 1.3 Mathematical models -- 1.3.1 Algebraic equations -- 1.3.2 ODE models -- 1.3.3 PDE models -- 1.3.4 Functional and integral equations -- 1.3.5 Discrete models -- 1.3.6 Statistical models -- 1.3.7 Data-driven models -- 1.4 Numerical models -- 1.4.1 Finite differences -- 1.4.2 Finite volumes -- 1.4.3 Finite elements -- 1.4.4 Meshless methods -- 1.4.5 Spectral methods -- 1.5 Notes on software -- 2 Ordinary differential equations -- 2.1 Ordinary differential equations -- 2.1.1 First-order ODEs -- 2.1.2 Higher-order ODEs -- 2.1.3 Differential operator and particular integrals -- 2.2 System of linear ODEs -- 2.3 Notes on software -- 3 Partial differential equations -- 3.1 First-order PDEs -- 3.2 Classification of second-order PDEs -- 3.3 Common PDEs in engineering -- 3.3.1 Heat conduction equation -- 3.3.2 Poisson's equation -- 3.3.3 Wave equation -- 3.4 Sound wave: a worked example -- 3.5 PDE solution techniques -- 3.5.1 Separation of variables -- 3.5.2 Laplace transform -- 3.6 Notes on software -- 4 Computational linear algebra -- 4.1 Vectors -- 4.2 Matrix algebra -- 4.3 System of linear equations -- 4.4 Eigenvalues and eigenvectors -- 4.5 Definite matrices -- 4.6 Iteration methods -- 4.6.1 Jacobi iteration method -- 4.6.2 Gauss-Seidel iteration -- 4.6.3 Relaxation method -- 4.7 Notes on software -- 5 Finite difference methods for ODEs -- 5.1 Integration of ODEs -- 5.2 Finite differences -- 5.2.1 Euler scheme -- 5.2.2 Numerical stability -- 5.2.3 Implicit Euler scheme -- 5.3 Leap-frog method -- 5.4 Runge-Kutta method -- 5.5 Shooting methods -- 5.6 Notes on software -- 6 Finite difference methods for PDEs -- 6.1 First-order PDEs. |
| Beschreibung: | 1 Online-Resource (240 Seiten) |
| ISBN: | 9780443140846 |
| DOI: | 10.1016/C2022-0-03141-X |
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| 520 | 3 | |a Front Cover -- Engineering Simulation and its Applications -- Copyright -- Contents -- About the author -- Preface -- Acknowledgments -- 1 Introduction to engineering simulation -- 1.1 Introduction -- 1.2 What is a model? -- 1.3 Mathematical models -- 1.3.1 Algebraic equations -- 1.3.2 ODE models -- 1.3.3 PDE models -- 1.3.4 Functional and integral equations -- 1.3.5 Discrete models -- 1.3.6 Statistical models -- 1.3.7 Data-driven models -- 1.4 Numerical models -- 1.4.1 Finite differences -- 1.4.2 Finite volumes -- 1.4.3 Finite elements -- 1.4.4 Meshless methods -- 1.4.5 Spectral methods -- 1.5 Notes on software -- 2 Ordinary differential equations -- 2.1 Ordinary differential equations -- 2.1.1 First-order ODEs -- 2.1.2 Higher-order ODEs -- 2.1.3 Differential operator and particular integrals -- 2.2 System of linear ODEs -- 2.3 Notes on software -- 3 Partial differential equations -- 3.1 First-order PDEs -- 3.2 Classification of second-order PDEs -- 3.3 Common PDEs in engineering -- 3.3.1 Heat conduction equation -- 3.3.2 Poisson's equation -- 3.3.3 Wave equation -- 3.4 Sound wave: a worked example -- 3.5 PDE solution techniques -- 3.5.1 Separation of variables -- 3.5.2 Laplace transform -- 3.6 Notes on software -- 4 Computational linear algebra -- 4.1 Vectors -- 4.2 Matrix algebra -- 4.3 System of linear equations -- 4.4 Eigenvalues and eigenvectors -- 4.5 Definite matrices -- 4.6 Iteration methods -- 4.6.1 Jacobi iteration method -- 4.6.2 Gauss-Seidel iteration -- 4.6.3 Relaxation method -- 4.7 Notes on software -- 5 Finite difference methods for ODEs -- 5.1 Integration of ODEs -- 5.2 Finite differences -- 5.2.1 Euler scheme -- 5.2.2 Numerical stability -- 5.2.3 Implicit Euler scheme -- 5.3 Leap-frog method -- 5.4 Runge-Kutta method -- 5.5 Shooting methods -- 5.6 Notes on software -- 6 Finite difference methods for PDEs -- 6.1 First-order PDEs. | |
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| id | DE-604.BV050069375 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-05T09:00:28Z |
| institution | BVB |
| isbn | 9780443140846 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035406793 |
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| physical | 1 Online-Resource (240 Seiten) |
| psigel | ZDB-33-EBS ZDB-33-EBS UBY_PDA_EBS_Kauf |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Academic Press |
| record_format | marc |
| spelling | Yang, Xin-She 1965- Verfasser (DE-588)1043733906 aut Engineering simulation and its applications algorithms and numerical methods Xin-She Yang London Academic Press 2024 1 Online-Resource (240 Seiten) txt rdacontent c rdamedia cr rdacarrier Front Cover -- Engineering Simulation and its Applications -- Copyright -- Contents -- About the author -- Preface -- Acknowledgments -- 1 Introduction to engineering simulation -- 1.1 Introduction -- 1.2 What is a model? -- 1.3 Mathematical models -- 1.3.1 Algebraic equations -- 1.3.2 ODE models -- 1.3.3 PDE models -- 1.3.4 Functional and integral equations -- 1.3.5 Discrete models -- 1.3.6 Statistical models -- 1.3.7 Data-driven models -- 1.4 Numerical models -- 1.4.1 Finite differences -- 1.4.2 Finite volumes -- 1.4.3 Finite elements -- 1.4.4 Meshless methods -- 1.4.5 Spectral methods -- 1.5 Notes on software -- 2 Ordinary differential equations -- 2.1 Ordinary differential equations -- 2.1.1 First-order ODEs -- 2.1.2 Higher-order ODEs -- 2.1.3 Differential operator and particular integrals -- 2.2 System of linear ODEs -- 2.3 Notes on software -- 3 Partial differential equations -- 3.1 First-order PDEs -- 3.2 Classification of second-order PDEs -- 3.3 Common PDEs in engineering -- 3.3.1 Heat conduction equation -- 3.3.2 Poisson's equation -- 3.3.3 Wave equation -- 3.4 Sound wave: a worked example -- 3.5 PDE solution techniques -- 3.5.1 Separation of variables -- 3.5.2 Laplace transform -- 3.6 Notes on software -- 4 Computational linear algebra -- 4.1 Vectors -- 4.2 Matrix algebra -- 4.3 System of linear equations -- 4.4 Eigenvalues and eigenvectors -- 4.5 Definite matrices -- 4.6 Iteration methods -- 4.6.1 Jacobi iteration method -- 4.6.2 Gauss-Seidel iteration -- 4.6.3 Relaxation method -- 4.7 Notes on software -- 5 Finite difference methods for ODEs -- 5.1 Integration of ODEs -- 5.2 Finite differences -- 5.2.1 Euler scheme -- 5.2.2 Numerical stability -- 5.2.3 Implicit Euler scheme -- 5.3 Leap-frog method -- 5.4 Runge-Kutta method -- 5.5 Shooting methods -- 5.6 Notes on software -- 6 Finite difference methods for PDEs -- 6.1 First-order PDEs. https://doi.org/10.1016/C2022-0-03141-X Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Yang, Xin-She 1965- Engineering simulation and its applications algorithms and numerical methods |
| title | Engineering simulation and its applications algorithms and numerical methods |
| title_auth | Engineering simulation and its applications algorithms and numerical methods |
| title_exact_search | Engineering simulation and its applications algorithms and numerical methods |
| title_full | Engineering simulation and its applications algorithms and numerical methods Xin-She Yang |
| title_fullStr | Engineering simulation and its applications algorithms and numerical methods Xin-She Yang |
| title_full_unstemmed | Engineering simulation and its applications algorithms and numerical methods Xin-She Yang |
| title_short | Engineering simulation and its applications |
| title_sort | engineering simulation and its applications algorithms and numerical methods |
| title_sub | algorithms and numerical methods |
| url | https://doi.org/10.1016/C2022-0-03141-X |
| work_keys_str_mv | AT yangxinshe engineeringsimulationanditsapplicationsalgorithmsandnumericalmethods |