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E-grāmata: Numerical Solution of Partial Differential Equations in Science and Engineering [Wiley Online]

  • Formāts: 696 pages, illustrations, bibliography, index
  • Izdošanas datums: 04-May-1982
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1118032969
  • ISBN-13: 9781118032961
  • Wiley Online
  • Cena: 211,85 €*
  • * this price gives unlimited concurrent access for unlimited time
  • Formāts: 696 pages, illustrations, bibliography, index
  • Izdošanas datums: 04-May-1982
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1118032969
  • ISBN-13: 9781118032961
From the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering:
* "The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject . . . [ It] is unique in that it covers equally finite difference and finite element methods."-Burrelle's.
* "The authors have selected an elementary (but not simplistic) mode of presentation. Many different computational schemes are described in great detail . . . Numerous practical examples and applications are described from beginning to the end, often with calculated results given."-Mathematics of Computing.
* "This volume . . . devotes its considerable number of pages to lucid developments of the methods [ for solving partial differential equations] . . . the writing is very polished and I found it a pleasure to read!"-Mathematics of Computation

Of related interest . . .NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen and Eli L. Isaacson. A modern, practical look at numerical analysis, this book guides readers through a broad selection of numerical methods, implementation, and basic theoretical results, with an emphasis on methods used in scientific computation involving differential equations. 1997 (0-471-55266-6) 512 pp.

APPLIED MATHEMATICS Second Edition, J. David Logan. Presenting an easily accessible treatment of mathematical methods for scientists and engineers, this acclaimed work covers fluid mechanics and calculus of variations as well as more modern methods-dimensional analysis and scaling, nonlinear wave propagation, bifurcation, and singular perturbation. 1996 (0-471-16513-1) 496 pp.
Fundamental Concepts
1(33)
Notation
1(3)
First-Order Partial Differential Equations
4(8)
First-Order Quasilinear Partial Differential Equations
4(2)
Initial Value or Cauchy Problem
6(1)
Application of Characteristic Curves
7(4)
Nonlinear First-Order Partial Differential Equations
11(1)
Second-Order Partial Differential Equations
12(9)
Linear Second-Order Partial Differential Equations
12(5)
Classification and Canonical Form of Selected Partial Differential Equations
17(1)
Quasilinear Partial Differential Equations and Other Ideas
17(4)
Systems of First-Order PDEs
21(7)
First-Order and Second-Order PDEs
21(3)
Characteristic Curves
24(2)
Applications of Characteristic Curves
26(2)
Initial and Boundary Conditions
28(6)
References
33(1)
Basic Concepts in the Finite Difference and Finite Element Methods
34(75)
Introduction
34(1)
Finite Difference Approximations
34(15)
Notation
35(1)
Taylor Series Expansions
36(2)
Operator Notation for u(x)
38(3)
Finite Difference Approximations in Two Dimensions
41(2)
Additional Concepts
43(6)
Introduction to Finite Element Approximations
49(55)
Method of Weighted Residuals
49(4)
Application of the Method of Weighted Residuals
53(7)
The Choice of Basis Functions
60(19)
Two-Dimensional Basis Functions
79(11)
Approximating Equations
90(14)
Relationship between Finite Element and Finite Difference Methods
104(5)
References
107(2)
Finite Elements on Irregular Subspaces
109(40)
Introduction
109(1)
Triangular Elements
109(11)
The Linear Triangular Element
109(1)
Area Coordinates
110(1)
The Quadratic Triangular Element
110(6)
The Cubic Triangular Element
116(4)
Higher-Order Triangular Elements
120(1)
Isoparametric Finite Elements
120(17)
Transformation Functions
120(6)
Numerical Integration
126(3)
Isoparametric Serendipity Hermitian Elements
129(2)
Isoparametric Hermitian Elements in Normal and Tangential Coordinates
131(6)
Boundary Conditions
137(4)
Three-Dimensional Elements
141(8)
References
148(1)
Parabolic Partial Differential Equations
149(206)
Introduction
149(1)
Partial Differential Equations
149(2)
Well-Posed Partial Differential Equations
151(1)
Model Difference Approximations
151(2)
Well-Posed Difference Forms
153(1)
Derivation of Finite Difference Approximations
153(9)
The Classic Explicit Approximation
155(2)
The Dufort-Frankel Explicit Approximation
157(1)
The Richardson Explicit Approximation
158(1)
The Backwards Implicit Approximation
159(1)
The Crank-Nicolson Implicit Approximation
160(1)
The Variable-Weighted Implicit Approximation
161(1)
Consistency and Convergence
162(4)
Stability
166(20)
Heuristic Stability
168(2)
Von Neumann Stability
170(9)
Matrix Stability
179(7)
Some Extensions
186(27)
Influence of Lower-Order Terms
186(1)
Higher-Order Forms
187(3)
Predictor-Corrector Methods
190(2)
Asymmetric Approximations
192(7)
Variable Coefficients
199(4)
Nonlinear Parabolic PDEs
203(8)
The Box Method
211(2)
Solution of Finite Difference Approximations
213(6)
Solution of Implicit Approximations
214(4)
Explicit versus Implicit Approximations
218(1)
Composite Solutions
219(15)
Global Extrapolation
220(4)
Some Numerical Results
224(2)
Local Combination
226(4)
Some Numerical Results
230(1)
Composites of Different Approximations
231(3)
Finite Difference Approximations in Two Space Dimensions
234(31)
Explicit Methods
234(6)
Irregular Boundaries
240(1)
Implicit Methods
241(3)
Alternating Direction Explicit (ADE) Methods
244(1)
Alternating Direction Implicit (ADI) Methods
245(10)
LOD and Fractional Splitting Methods
255(6)
Hopscotch Methods
261(3)
Mesh Refinement
264(1)
Three-Dimensional Problems
265(11)
ADI Methods
266(6)
LOD and Fractional Splitting Methods
272(2)
Iterative Solutions
274(2)
Finite Element Solution of Parabolic Partial Differential Equations
276(9)
Galerkin Approximation to the Model Parabolic Partial Differential Equation
277(3)
Approximation of the Time Derivative
280(2)
Approximation of the Time Derivative for Weakly Nonlinear Equations
282(3)
Finite Element Approximations in One Space Dimensions
285(24)
Formulation of the Galerkin Approximating Equations
285(4)
Linear Basis Function Approximation
289(5)
Higher-Degree Polynomial Basis Function Approximation
294(3)
Formulation Using the Dirac Delta Function
297(2)
Orthogonal Collocation Formulation
299(7)
Asymmetric Weighting Functions
306(3)
Finite Element Approximations in Two Space Dimensions
309(39)
Galerkin Approximation in Space and Time
309(5)
Galerkin Approximation in Space Finite Difference in Time
314(2)
Asymmetric Weighting Functions in Two Space Dimensions
316(5)
Lumped and Consistent Time Matrices
321(9)
Collocation Finite Element Formulation
330(9)
Treatment of Sources and Sinks
339(3)
Alternating Direction Formulation
342(6)
Finite Element Approximations in Three Space Dimensions
348(2)
Example Problem
348(2)
Summary
350(5)
References
351(4)
Elliptic Partial Differential Equations
355(131)
Introduction
355(1)
Model Elliptic PDEs
355(5)
Specific Elliptic PDEs
355(1)
Boundary Conditions
356(2)
Further Items
358(2)
Finite Difference Solutions in Two Space Dimensions
360(74)
Five-Point Approximations and Truncation Error
360(11)
Nine-Point Approximations and Truncation Error
371(2)
Approximations to the Biharmonic Equation
373(2)
Boundary Condition Approximations
375(2)
Matrix Form of Finite Difference Equations
377(6)
Direct Methods of Solution
383(2)
Iterative Concepts
385(7)
Formulation of Point Iterative Methods
392(13)
Convergence of Point Iterative Methods
405(13)
Line and Block Iteration Methods
418(3)
ADI Methods
421(9)
Acceleration and Semi-Iterative Overlays
430(4)
Finite Difference Solutions in Three Space Dimensions
434(7)
Finite Difference Approximations
435(2)
Iteration Concepts
437(1)
ADI Methods
437(4)
Finite Element Methods for Two Space Dimensions
441(20)
Galerkin Approximation
442(3)
Example Problem
445(4)
Collocation Approximation
449(4)
Mixed Finite Element Approximation
453(2)
Approximation of the Biharmonic Equation
455(6)
Boundary Integral Equation Methods
461(20)
Fundamental Theory
461(4)
Boundary Element Formulation
465(2)
Example Problem
467(4)
Linear Interpolation Functions
471(2)
Poisson's Equation
473(2)
Nonhomogeneous Materials
475(3)
Combination of Finite Element and Boundary Integral Equation Methods
478(3)
Three-Dimensional Finite Element Simulation
481(1)
Summary
482(4)
References
482(4)
Hyperbolic Partial Differential Equations
486(185)
Introduction
486(1)
Equations of Hyperbolic Type
487(2)
Finite Difference Solution of First-Order Scalar Hyperbolic Partial Differential Equations
489(37)
Stability, Truncation Error, and Other Features
490(7)
Other Approximations
497(8)
Dissipation and Dispersion
505(19)
Hopscotch Methods and Mesh Refinement
524(2)
Finite Difference Solution of First-Order Vector Hyperbolic Partial Differential Equations
526(2)
Finite Difference Solution of First-Order Vector Conservative Hyperbolic Partial Differential Equations
528(11)
Finite Difference Solutions to Two-and Three-Dimensional Hyperbolic Partial Differential Equations
539(23)
Finite Difference Schemes
540(5)
Two-Step, ADI, and Strang-Type Algorithms
545(9)
Conservative Hyperbolic Partial Differential Equations
554(8)
Finite Difference Solution of Second-Order Model Hyperbolic Partial Differential Equations
562(27)
One-Space-Dimension Hyperbolic Partial Differential Equation
562(2)
Explicit Algorithms
564(5)
Implicit Algorithms
569(2)
Simultaneous First-Order Partial Differential Equations
571(6)
Mixed Systems
577(3)
Two-and Three-Space-Dimensional Hyperbolic Partial Differential Equations
580(3)
Implicit ADI and LOD Methods
583(6)
Finite Element Solution of First-Order Model Hyperbolic Partial Differential Equations
589(31)
Galerkin Approximation
589(5)
Asymmetric Weighting Function Approximation
594(4)
An H++ Galerkin Approximation
598(1)
Orthogonal Collocation Formulation
599(5)
Orthogonal Collocation with Asymmetric Bases
604(1)
Dissipation and Dispersion
605(15)
Finite Element Solution of Two-and Three-Space-Dimensional First-Order Hyperbolic Partial Differential Equations
620(5)
Galerkin Finite Element Formulation
620(2)
Orthogonal Collocation Formulation
622(3)
Finite Element Solution of First-Order Vector Hyperbolic Partial Differential Equations
625(20)
Galerkin Finite Element Formulation
626(1)
Dissipation and Dispersion
627(18)
Finite Element Solution of Two-and Three-Space-Dimensional First-Order Vector Hyperbolic Partial Differential Equations
645(10)
Galerkin Finite Element Formulation
645(3)
Boundary Conditions
648(7)
Finite Element Solution of One-Space-Dimensional Second-Order Hyperbolic Partial Differential Equations
655(10)
Galerkin Finite Element Formulation
655(2)
Time Approximations
657(6)
Dissipation and Dispersion
663(2)
Finite Element Solution of Two-and Three-Space-Dimensional Second-Order Hyperbolic Partial Differential Equations
665(2)
Galerkin Finite Element Formulation
665(2)
Summary
667(4)
References
667(4)
Index 671