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Computational Partial Differential Equations Using MATLAB® 2nd edition [Kõva köide]

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(University of Nevada-Las Vegas), (University of Nevada-Las Vegas)
  • Formaat: Hardback, 422 pages, kõrgus x laius: 234x156 mm, kaal: 762 g, 8 Tables, black and white; 43 Illustrations, black and white
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 11-Oct-2019
  • Kirjastus: CRC Press
  • ISBN-10: 0367217740
  • ISBN-13: 9780367217747
Teised raamatud teemal:
Computational Partial Differential Equations Using MATLAB® 2nd editionSuurem pilt
  • Formaat: Hardback, 422 pages, kõrgus x laius: 234x156 mm, kaal: 762 g, 8 Tables, black and white; 43 Illustrations, black and white
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 11-Oct-2019
  • Kirjastus: CRC Press
  • ISBN-10: 0367217740
  • ISBN-13: 9780367217747
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367217747.html
Märksõnad:

In this popular text for an Numerical Analysis course, the authors introduce several major methods of solving various partial differential equations (PDEs) including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques including the classic finite difference method, finite element method, and state-of-the-art numercial methods.The text uniquely emphasizes both theoretical numerical analysis and practical implementation of the algorithms in MATLAB. This new edition includes a new chapter, Finite Value Method, the presentation has been tightened, new exercises and applications are included, and the text refers now to the latest release of MATLAB.

 

Key Selling Points:

 

  • A successful textbook for an undergraduate text on numerical analysis or methods taught in mathematics and computer engineering.
  • This course is taught in every university throughout the world with an engineering department or school.
  • Competitive advantage broader numerical methods (including finite difference, finite element, meshless method, and finite volume method), provides the MATLAB source code for most popular PDEs with detailed explanation about the implementation and theoretical analysis. No other existing textbook in the market offers a good combination of theoretical depth and practical source codes.
Preface xi
Acknowledgments xiii
1 Brief Overview of Partial Differential Equations
1(12)
1.1 The parabolic equations
1(1)
1.2 The wave equations
2(1)
1.3 The elliptic equations
3(1)
1.4 Differential equations in broader areas
3(6)
1.4.1 Electromagnetics
3(1)
1.4.2 Fluid mechanics
4(1)
1.4.3 Groundwater contamination
5(1)
1.4.4 Petroleum reservoir simulation
6(1)
1.4.5 Finance modeling
7(1)
1.4.6 Image processing
8(1)
1.5 A quick review of numerical methods for PDEs
9(4)
References
11(2)
2 Finite Difference Methods for Parabolic Equations
13(30)
2.1 Introduction
13(3)
2.2 Theoretical issues: stability, consistence, and convergence
16(2)
2.3 1-D parabolic equations
18(9)
2.3.1 The θ-method and its analysis
18(5)
2.3.2 Some extensions
23(4)
2.4 2-D and 3-D parabolic equations
27(8)
2.4.1 Standard explicit and implicit methods
27(3)
2.4.2 The ADI methods for 2-D problems
30(2)
2.4.3 The ADI methods for 3-D problems
32(3)
2.5 Numerical examples with MATLAB codes
35(2)
2.6 Bibliographical remarks
37(1)
2.7 Exercises
38(5)
References
41(2)
3 Finite Difference Methods for Hyperbolic Equations
43(22)
3.1 Introduction
43(1)
3.2 Some basic difference schemes
44(3)
3.3 Dissipation and dispersion errors
47(2)
3.4 Extensions to conservation laws
49(1)
3.5 The second-order hyperbolic equations
50(7)
3.5.1 The 1-D case
50(3)
3.5.2 The 2-D case
53(4)
3.6 Numerical examples with MATLAB codes
57(2)
3.7 Bibliographical remarks
59(1)
3.8 Exercises
60(5)
References
62(3)
4 Finite Difference Methods for Elliptic Equations
65(24)
4.1 Introduction
65(2)
4.2 Numerical solution of linear systems
67(7)
4.2.1 Direct methods
67(2)
4.2.2 Simple iterative methods
69(3)
4.2.3 Modern iterative methods
72(2)
4.3 Error analysis with a maximum principle
74(2)
4.4 Some extensions
76(5)
4.4.1 Mixed boundary conditions
77(1)
4.4.2 Self-adjoint problems
78(1)
4.4.3 A fourth-order scheme
78(3)
4.5 Numerical examples with MATLAB codes
81(3)
4.6 Bibliographical remarks
84(1)
4.7 Exercises
84(5)
References
86(3)
5 High-Order Compact Difference Methods
89(56)
5.1 One-dimensional problems
89(32)
5.1.1 Spatial discretization
89(5)
5.1.2 Dispersive error analysis
94(4)
5.1.3 Temporal discretization
98(5)
5.1.4 Low-pass spatial filter
103(1)
5.1.5 Numerical examples with MATLAB codes
104(17)
5.2 High-dimensional problems
121(12)
5.2.1 Temporal discretization for 2-D problems
121(2)
5.2.2 Stability analysis
123(1)
5.2.3 Extensions to 3-D compact ADI schemes
124(1)
5.2.4 Numerical examples with MATLAB codes
125(8)
5.3 Other high-order compact schemes
133(5)
5.3.1 One-dimensional problems
133(2)
5.3.2 Two-dimensional problems
135(3)
5.4 Bibliographical remarks
138(1)
5.5 Exercises
138(7)
References
141(4)
6 Finite Element Methods: Basic Theory
145(48)
6.1 Introduction to one-dimensional problems
145(7)
6.1.1 The second-order equation
145(3)
6.1.2 The fourth-order equation
148(4)
6.2 Introduction to two-dimensional problems
152(3)
6.2.1 The Poisson equation
152(2)
6.2.2 The biharmonic problem
154(1)
6.3 Abstract finite element theory
155(3)
6.3.1 Existence and uniqueness
156(1)
6.3.2 Stability and convergence
157(1)
6.4 Examples of conforming finite element spaces
158(6)
6.4.1 Triangular finite elements
159(4)
6.4.2 Rectangular finite elements
163(1)
6.5 Examples of nonconforming finite elements
164(3)
6.5.1 Nonconforming triangular elements
164(1)
6.5.2 Nonconforming rectangular elements
165(2)
6.6 Finite element interpolation theory
167(6)
6.6.1 Sobolev spaces
167(2)
6.6.2 Interpolation theory
169(4)
6.7 Finite element analysis of elliptic problems
173(4)
6.7.1 Analysis of conforming finite elements
173(2)
6.7.2 Analysis of nonconforming finite elements
175(2)
6.8 Finite element analysis of time-dependent problems
177(8)
6.8.1 Introduction
177(1)
6.8.2 FEM for parabolic equations
178(7)
6.9 Bibliographical remarks
185(1)
6.10 Exercises
186(7)
References
188(5)
7 Finite Element Methods: Programming
193(26)
7.1 FEM mesh generation
193(5)
7.2 Forming FEM equations
198(1)
7.3 Calculation of element matrices
199(5)
7.4 Assembly and implementation of boundary conditions
204(1)
7.5 The MATLAB code for P1 element
205(3)
7.6 The MATLAB code for the Q1 element
208(5)
7.7 Bibliographical remarks
213(1)
7.8 Exercises
214(5)
References
217(2)
8 Mixed Finite Element Methods
219(42)
8.1 An abstract formulation
219(4)
8.2 Mixed methods for elliptic problems
223(9)
8.2.1 The mixed variational formulation
223(2)
8.2.2 The mixed finite element spaces
225(4)
8.2.3 The error estimates
229(3)
8.3 Mixed methods for the Stokes problem
232(20)
8.3.1 The mixed variational formulation
232(6)
8.3.2 Mixed finite element spaces
238(14)
8.4 An example MATLAB code for the Stokes problem
252(1)
8.5 Mixed methods for viscous incompressible flows
252(4)
8.5.1 The steady Navier-Stokes problem
254(1)
8.5.2 The unsteady Navier-Stokes problem
255(1)
8.6 Bibliographical remarks
256(1)
8.7 Exercises
256(5)
References
259(2)
9 Finite Element Methods for Electromagnetics
261(70)
9.1 Introduction to Maxwell's equations
261(2)
9.2 The time-domain finite difference method
263(22)
9.2.1 The semi-discrete scheme
263(9)
9.2.2 The fully discrete scheme
272(13)
9.3 The time-domain finite element method
285(13)
9.3.1 The mixed method
285(5)
9.3.2 The standard Galerkin method
290(3)
9.3.3 The discontinuous Galerkin method
293(5)
9.4 The frequency-domain finite element method
298(7)
9.4.1 The standard Galerkin method
298(1)
9.4.2 The discontinuous Galerkin method
299(4)
9.4.3 The mixed DG method
303(2)
9.5 Maxwell's equations in dispersive media
305(18)
9.5.1 Isotropic cold plasma
306(4)
9.5.2 Debye medium
310(3)
9.5.3 Lorentz medium
313(2)
9.5.4 Double-negative metamaterials
315(8)
9.6 Bibliographical remarks
323(1)
9.7 Exercises
324(7)
References
325(6)
10 Meshless Methods with Radial Basis Functions
331(48)
10.1 Introduction
331(1)
10.2 The radial basis functions
332(3)
10.3 The MFS-DRM
335(13)
10.3.1 The fundamental solution of PDEs
335(3)
10.3.2 The MFS for Laplace's equation
338(3)
10.3.3 The MFS-DRM for elliptic equations
341(3)
10.3.4 Computing particular solutions using RBFs
344(2)
10.3.5 The RBF-MFS
346(1)
10.3.6 The MFS-DRM for the parabolic equations
346(2)
10.4 Kansa s method
348(4)
10.4.1 Kansa's method for elliptic problems
348(1)
10.4.2 Kansa's method for parabolic equations
349(1)
10.4.3 The Hermite-Birkhoff collocation method
350(2)
10.5 Numerical examples with MATLAB codes
352(14)
10.5.1 Elliptic problems
352(7)
10.5.2 Biharmonic problems
359(7)
10.6 Coupling RBF meshless methods with DDM
366(6)
10.6.1 Overlapping DDM
367(1)
10.6.2 Non-overlapping DDM
368(1)
10.6.3 One numerical example
369(3)
10.7 Bibliographical remarks
372(1)
10.8 Exercises
372(7)
References
373(6)
11 Other Meshless Methods
379(14)
11.1 Construction of meshless shape functions
379(5)
11.1.1 The smooth particle hydrodynamics method
379(2)
11.1.2 The moving least-square approximation
381(1)
11.1.3 The partition of unity method
382(2)
11.2 The element-free Galerkin method
384(2)
11.3 The meshless local Petrov-Galerkin method
386(3)
11.4 Bibliographical remarks
389(1)
11.5 Exercises
389(4)
References
390(3)
Appendix A Answers to Selected Problems 393(12)
Index 405
Jichun Li ia a professor of mathematics at the University of Nevada, Las Vegas. He earned a Ph.D in Applied Mathematics from Florida State University and in addition to authoring several journal papers and three other books, he is a founding editor-in-chief of Results in Applied Mathematics. His major research areas are on numerical methods for partial differential equations.

Yi-Tung Chen is the co-director for the Center for Energy Research at the University of Nevada, Las Vegas. He has a Ph.D. from the University of Utah and is an aerial systems expert in computational fluid dynamics, fluid-structure interaction and aerodynamics.