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 --...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Yang, Xin-She 1965- (VerfasserIn)
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