Advanced Numerical Methods with Matlab 2

Name: Advanced Numerical Methods with Matlab 2 | Resolution of Nonlinear, Differential and Partial Differential Equations
Brand: Wiley-Blackwell
Price: 139.99 EUR
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Resolution of Nonlinear, Differential and Partial Differential Equations

Radi Bouchaib Abdelkhalak El Hami(Autor*in)

Wiley-Blackwell (Verlag)

1. Auflage

Erschienen am 23. Mai 2018

224 Seiten

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978-1-119-52741-1 (ISBN)

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Inhalt

Cover
Half-Title Page
Title Page
Copyright Page
Contents
Preface
PART 1 Solving Equations
1. Solving Nonlinear Equations
1.1. Introduction
1.2. Separating the roots
1.3. Approximating a separated root
1.3.1. Bisection method (or dichotomy method)
1.3.2. Fixed-point method
1.3.3. First convergence criterion
1.3.4. Iterative stopping criteria
1.3.5. Second convergence criterion (local criterion)
1.3.6. Newton's method (or the method of tangents)
1.3.7. Secant method
1.3.8. Regula falsi method (or false position method)
1.4. Order of an iterative process
1.5. Using Matlab
1.5.1. Finding the roots of polynomials
1.5.2. Bisection method
1.5.3. Newton's method
2. Numerically Solving Differential Equations
2.1. Introduction
2.2. Cauchy problem and discretization
2.3. Euler's method
2.3.1. Interpretation
2.3.2. Convergence
2.4. One-step Runge-Kutta method
2.4.1. Second-order Runge-Kutta method
2.4.2. Fourth-order Runge-Kutta method
2.5. Multi-step Adams methods
2.5.1. Open Adams methods
2.5.2. Closed Adams formulas
2.6. Predictor-Corrector method
2.7. Using Matlab
PART 2 Solving PDEs
3. Finite Difference Methods
3.1. Introduction
3.2. Presentation of the finite difference method
3.2.1. Convergence, consistency and stability
3.2.2. Courant-Friedrichs-Lewy condition
3.2.3. Von Neumann stability analysis
3.3. Hyperbolic equations
3.3.1. Key results
3.3.2. Numerical schemes for solving the transport equation
3.3.3. Wave equation
3.3.4. Burgers equation
3.4. Elliptic equations
3.4.1. Poisson equation
3.5. Parabolic equations
3.5.1. Heat equation
3.6. Using Matlab
4. Finite Element Method
4.1. Introduction
4.2. One-dimensional finite element methods
4.3. Two-dimensional finite element methods
4.4. General procedure of the method
4.5. Finite element method for computing elastic structures
4.5.1. Linear elasticity
4.5.2. Variational formulation of the linear elasticity problem
4.5.3. Planar linear elasticity problems
4.5.4. Applying the finite element method to planar problems
4.5.5. Axisymmetric problems
4.5.6. Three-dimensional problems
4.6. Using Matlab
4.6.1. Solving Poisson's equation
4.6.2. Solving the heat equation
4.6.3. Computing structures
5. Finite Volume Methods
5.1. Introduction
5.2. Finite volume method (FVM)
5.2.1. Conservation properties of the method
5.2.2. The stages of the method
5.2.3. Convergence
5.2.4. Consistency
5.2.5. Stability
5.3. Advection schemes
5.3.1. Two-dimensional FVM
5.3.2. Convection-diffusion equation
5.3.3. Central differencing scheme
5.3.4. Upwind (decentered) scheme
5.3.5. Hybrid scheme
5.3.6. Power-law scheme
5.3.7. QUICK scheme
5.3.8. Higher-order schemes
5.3.9. Unsteady one-dimensional convection-diffusion equation
5.3.10. Explicit scheme
5.3.11. Crank-Nicolson scheme
5.3.12. Implicit scheme
5.4. Using Matlab
6. Meshless Methods
6.1. Introduction
6.2. Limitations of the FEM and motivation of meshless methods
6.3. Examples of meshless methods
6.3.1. Advantages of meshless methods
6.3.2. Disadvantages of meshless methods
6.3.3. Comparison of the finite element method and meshless methods
6.4. Basis of meshless methods
6.4.1. Approximations
6.4.2. Kernel (weight) functions
6.4.3. Completeness
6.4.4. Partition of unity
6.5. Meshless method (EFG)
6.5.1. Theory
6.5.2. Moving Least-Squares Approximation
6.6. Application of the meshless method to elasticity
6.6.1. Formulation of static linear elasticity
6.6.2. Imposing essential boundary conditions
6.7. Numerical examples
6.7.1. Fixed-free beam
6.7.2. Compressed block
6.8. Using Matlab
PART 3 Appendices
Appendix 1 Introduction to Matlab
A1.1. Introduction
A1.2. Starting up Matlab
A1.3. Mathematical functions
A1.4. Operators and programming with Matlab
A1.5. Writing a Matlab script
A1.6. Generating figures with Matlab
Appendix 2 General Approximation Principles
A2.1. Standard results
A2.2. Linear variational problems
A2.3. Variational approximation
A2.4. General result on an upper bound for the error
A2.5. Speed of convergence
A2.6. Galerkin method
Bibliography
Index
Other titles from iSTE in Mechanical Engineering and Solid Mechanics
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