Muutke küpsiste eelistusi

Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB: Scientific and Engineering Applications 2014 ed. [Kõva köide]

, ,
  • Formaat: Hardback, 406 pages, kõrgus x laius: 235x155 mm, kaal: 8336 g, 33 Illustrations, color; 108 Illustrations, black and white; XV, 406 p. 141 illus., 33 illus. in color. With online files/update., 1 Hardback
  • Ilmumisaeg: 01-Jul-2014
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319067893
  • ISBN-13: 9783319067896
Teised raamatud teemal:
  • Kõva köide
  • Hind: 150,61 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Tavahind: 177,19 €
  • Säästad 15%
  • Raamatu kohalejõudmiseks kirjastusest kulub orienteeruvalt 2-4 nädalat
  • Kogus:
  • Lisa ostukorvi
  • Tasuta tarne
  • Tellimisaeg 2-4 nädalat
  • Lisa soovinimekirja
Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB: Scientific and Engineering Applications 2014 ed.Suurem pilt
  • Formaat: Hardback, 406 pages, kõrgus x laius: 235x155 mm, kaal: 8336 g, 33 Illustrations, color; 108 Illustrations, black and white; XV, 406 p. 141 illus., 33 illus. in color. With online files/update., 1 Hardback
  • Ilmumisaeg: 01-Jul-2014
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319067893
  • ISBN-13: 9783319067896
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319067896.html
Märksõnad:
Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration.

Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs.

Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the books page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.
1 An Introductory Tour 1(44)
1.1 Some ODE Applications
1(31)
1.2 An ODE/DAE Application
32(5)
1.3 A PDE Application
37(6)
1.4 Summary
43(1)
References
44(1)
2 More on ODE Integration 45(80)
2.1 A Basic Fixed Step ODE Integrator
45(6)
2.2 A Basic Variable-Step Nonstiff ODE Integrator
51(16)
2.3 A Basic Variable Step Implicit ODE Integrator
67(18)
2.4 MATLAB ODE Suite
85(1)
2.5 Some Additional ODE Applications
86(23)
2.5.1 Spruce Budworm Dynamics
86(7)
2.5.2 Liming to Remediate Acid Rain
93(16)
2.6 On the Use of SCILAB and OCTAVE
109(6)
2.7 How to Use Your Favorite Solvers in MATLAB?
115(8)
2.7.1 A Simple Example: Matrix Multiplication
117(5)
2.7.2 MEX-Files for ODE Solvers
122(1)
2.8 Summary
123(1)
References
123(2)
3 Finite Differences and the Method of Lines 125(78)
3.1 Basic Finite Differences
126(1)
3.2 Basic MOL
127(2)
3.3 Numerical Stability: Von Neumann and the Matrix Methods
129(7)
3.4 Numerical Study of the Advection Equation
136(6)
3.5 Numerical Study of the Advection-Diffusion Equation
142(8)
3.6 Numerical Study of the Advection-Diffusion-Reaction Equation
150(1)
3.7 Is it Possible to Enhance Stability?
151(2)
3.8 Stiffness
153(4)
3.9 Accuracy and the Concept of Differentiation Matrices
157(10)
3.10 Various Ways of Translating the Boundary Conditions
167(23)
3.10.1 Elimination of Unknown Variables
170(4)
3.10.2 Fictitious Nodes
174(2)
3.10.3 Solving Algebraic Equations
176(3)
3.10.4 Tricks Inspired by the Previous Methods
179(2)
3.10.5 An Illustrative Example (with Several Boundary Conditions)
181(9)
3.11 Computing the Jacobian Matrix of the ODE System
190(7)
3.12 Solving PDEs Using SCILAB and OCTAVE
197(3)
3.13 Summary
200(1)
References
201(2)
4 Finite Elements and Spectral Methods 203(82)
4.1 The Methods of Weighted Residuals
211(4)
4.1.1 Interior Method
213(1)
4.1.2 Boundary Method
213(1)
4.1.3 Mixed Method
213(1)
4.1.4 Galerkin Method
214(1)
4.1.5 Collocation Method
214(1)
4.1.6 Orthogonal Collocation Method
214(1)
4.2 The Basics of the Finite Element Method
215(1)
4.3 Galerkin Method Over Linear Lagrangian Elements
216(11)
4.3.1 LHS of the Weighted Residual Solution
218(1)
4.3.2 First Term in the RHS of the Weighted Residual Solution
219(1)
4.3.3 Second Term in the RHS of the Weighted Residual Solution
220(1)
4.3.4 Third Term in the RHS of the Weighted Residual Solution
221(3)
4.3.5 Fourth Term in the RHS of the Weighted Residual Solution
224(3)
4.4 Galerkin Method Over Linear Lagrangian Elements: Contribution of the Boundary Conditions
227(2)
4.4.1 Dirichlet Boundary Conditions
228(1)
4.4.2 Neumann Boundary Conditions
228(1)
4.5 The Finite Element Method in Action
229(6)
4.6 The Finite Element Method Applied to Systems of PDEs
235(2)
4.7 Galerkin Method Over Hermitian Elements
237(8)
4.7.1 LHS Term of the Weighted Residual Solution
237(2)
4.7.2 First and Second Terms of the RHS Term of the Weighted Residual Solution
239(2)
4.7.3 Third Term of the RHS Term of the Weighted Residual Solution
241(1)
4.7.4 Fourth Term of the RHS Term of the Weighted Residual Solution
242(1)
4.7.5 Galerkin Method Over Hermitian Elements: Contribution of the Boundary Conditions
243(2)
4.8 An Illustrative Example
245(4)
4.9 The Orthogonal Collocation Method
249(7)
4.9.1 LHS Term of the Collocation Residual Equation
251(1)
4.9.2 First Three Terms of Collocation Residual Equation
252(2)
4.9.3 Fourth Term of the RHS of the Collocation Residual Equation
254(1)
4.9.4 Contribution of the Boundary Conditions
255(1)
4.9.5 A Brief Benchmark
256(1)
4.10 Chebyshev Collocation
256(6)
4.11 The Proper Orthogonal Decomposition
262(15)
4.11.1 The Method of Snapshots
265(3)
4.11.2 Example: The Heat Equation
268(5)
4.11.3 Example: The Brusselator
273(4)
4.12 On the Use of SCILAB and OCTAVE
277(5)
4.13 Summary
282(1)
References
282(3)
5 How to Handle Steep Moving Fronts? 285(54)
5.1 Conservation Laws
286(2)
5.2 The Methods of Characteristics and of Vanishing Viscosity
288(5)
5.3 Transformation-Based Methods
293(2)
5.4 Upwind Finite Difference and Finite Volume Schemes
295(3)
5.5 A Divide and Conquer Approach
298(5)
5.6 Finitt Volume Methods and Slope Limiters
303(18)
5.7 Grid Refinement
321(10)
5.8 An Additional PDE Application
331(3)
5.9 Summary
334(1)
References
335(4)
6 Two Dimensional and Time Varying Spatial Domains 339(64)
6.1 Solution of Partial Differential Equations in More than 1D Using Finite Differences
339(22)
6.1.1 The Heat Equation on a Rectangle
340(4)
6.1.2 Graetz Problem with Constant Wall Temperature
344(4)
6.1.3 Tubular Chemical Reactor
348(4)
6.1.4 Heat Equation on a Convex Quadrilateral
352(5)
6.1.5 A Convection-Diffusion Equation on a Square
357(3)
6.1.6 Burgers Equation on a Square
360(1)
6.2 Solution of 2D PDEs Using Finite Element Techniques
361(27)
6.2.1 FitzHugh-Nagumo' s Model
364(18)
6.2.2 Reduced-Order Model for FitzHugh-Nagumo Model
382(6)
6.3 Solution of PDEs on Time-Varying Domains
388(11)
6.3.1 The Freeze-Drying Model
389(2)
6.3.2 The Landau Transform
391(3)
6.3.3 The Finite Element Representation
394(5)
6.4 Summary
399(1)
References
400(3)
Index 403