Screen LibraryNumerical methods for partial differential equations /
This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirement...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
Academic Press,
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| Publisher Address: | Boston : |
| Publication Dates: | 1992. |
| Literature type: | eBook |
| Language: | English |
| Edition: | Third edition. |
| Series: |
Computer science and scientific computing
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| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/book/9780080571300 |
| Summary: |
This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was publish |
| Carrier Form: | 1 online resource (ix, 451 pages) : illustrations. |
| Bibliography: | Includes bibliographical references and indexes. |
| ISBN: |
9780080571300 0080571301 |
| Index Number: | QA374 |
| CLC: | O175.2 |
| Contents: |
Front Cover; Numerical Methods for Partial Differential Equations; Copyright Page; Table of Contents; Preface to the Third Edition; Preface to the Second Edition; Preface to the First Edition; Chapter 1. Fundamentals; 1-0 Introduction; 1-1 Computer Program Packages; 1-2 Typical Problems; 1-3 Classification of Equations; 1-4 Discrete Methods; 1-5 Finite Differences and Computational Molecules; 1-6 Finite Difference Operators; 1-7 Method of Weighted Residuals; 1-8 Finite Elements; 1-9 Method of Lines; 1-10 Errors; 1-11 Stability and Convergence; 1-12 Irregular Boundaries. 1-13 Choice of Discrete Network1-14 Dimensionless Forms; References; Chapter 2. Parabolic Equations; 2-0 Introduction; 2-1 Properties of a Simple Explicit Method; 2-2 Fourier Stability Method; 2-3 Implicit Methods; 2-4 Additional Stability Considerations; 2-5 Matrix Stability Analysis; 2-6 Extension of Matrix Stability Analysis; 2-7 Consistency, Stability, and Convergence; 2-8 Pure Initial Value Problems; 2-9 Variable Coefficients; 2-10 Examples of Equations with Variable Coefficients; 2-11 General Concepts of Error Reduction; 2-12 Methods of Lines (MOL) for Parabolic Equations. 2-13 Weighted Residuals and the Method of Lines2-14 Bubnov-Galerkin Scheme for Parabolic Equations; 2-15 Finite Elements and Parabolic Equations-Hermite Basis; 2-16 Finite Elements and Parabolic Equations-General Basis Functions; 2-17 Finite Elements and Parabolic Equations-Special Basis Functions; 2-18 Explicit Finite Difference Methods for Nonlinear Problems; 2-19 An Application of the Explicit Method; 2-20 Implicit Methods for Nonlinear Problems; 2-21 Further Applications in One Dimension; 2-22 Asymmetric Approximations; References; Chapter 3. Elliptic Equations; 3-0 Introduction. 3-1 Simple Finite Difference Schemes3-2 Direct Methods; 3-3 Iterative Methods; 3-4 Linear Elliptic Equations; 3-5 Some Point Iterative Methods; 3-6 Convergence of Point Iterative Methods; 3-7 Rates of Convergence; 3-8 Accelerations; 3-9 Conjugate Gradient Method; 3-10 Extensions of SOR; 3-11 Qualitative Examples of Over-Relaxation; 3-12 Other Point Iterative Methods; 3-13 Block Iterative Methods; 3-14 Alternating Direction Methods; 3-15 Summary of ADI Results; 3-16 Triangular Elements; 3-17 Boundary Element Method (BEM); 3-18 Spectral Methods; 3-19 Some Nonlinear Examples; References. Chapter 4. Hyperbolic Equations4-0 Introduction; 4-1 The Quasilinear System; 4-2 Introductory Examples; 4-3 Method of Characteristics; 4-4 Constant States and Simple Waves; 4-5 Typical Application of Characteristics; 4-6 Finite Differences for First-Order Equations; 4-7 Lax-Wendroff Methods and Other Algorithms; 4-8 Dissipation and Dispersion; 4-9 Explicit Finite Difference Methods; 4-10 Attenuation; 4-11 Implicit Methods for Second-Order Equations; 4-12 Time Quasilinear Examples; 4-13 Simultaneous First-Order Equations-Explicit Methods; 4-14 An Implicit Method for First-Order Equations. |