The numerical solution of ordinary and partial differential equations /

The numerical solution of ordinary and partial differential equations /

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Bibliographic Details
Main Author: Sewell, Granville (Author)
Format: Book
Language:English
Published: New Jersey : World Scientific, [2015]
Singapore ; Hackensack, NJ : [2015]
Edition:3rd edition
Subjects:
Differential equations > Numerical solutions > Data processing
Differential equations, Partial > Numerical solutions > Data processing
Differential equations, Partial > Numerical solutions
Table of Contents:
  • note: 0 Direct Solution of Linear Systems
  • 0.0. Introduction
  • 0.1. General Linear Systems
  • 0.2. Systems Requiring No Pivoting
  • 0.3. L U Decomposition
  • 0.4. Banded Linear Systems
  • 0.5. Sparse Direct Methods
  • 0.6. Problems
  • 1. Initial Value Ordinary Differential Equations
  • 1.0. Introduction
  • 1.1. Euler's Method
  • 1.2. Truncation Error, Stability, and Convergence
  • 1.3. Multistep Methods
  • 1.4. Adams Multistep Methods
  • 1.5. Backward Difference Methods for Stiff Problems
  • 1.6. Runge-Kutta Methods
  • 1.7. Problems
  • 2. Initial Value Diffusion Problem
  • 2.0. Introduction
  • 2.1. Explicit Method
  • 2.2. Implicit Methods
  • 2.3. One-Dimensional Example
  • 2.4. Multidimensional Problems
  • 2.5. Diffusion-Reaction Example
  • 2.6. Problems
  • 3. Initial Value Transport and Wave Problems
  • 3.0. Introduction
  • 3.1. Explicit Methods for the Transport Problem
  • 3.2. Method of Characteristics
  • 3.3. Explicit Method for the Wave Equation
  • 3.4. Damped Wave Example
  • 3.5. Problems
  • 4. Boundary Value Problems
  • 4.0. Introduction
  • 4.1. Finite Difference Methods
  • 4.2. Nonlinear Example
  • 4.3. Singular Example
  • 4.4. Shooting Methods
  • 4.5. Multidimensional Problems
  • 4.6. Successive Overrelaxation
  • 4.7. Successive Overrelaxation Examples
  • 4.8. Conjugate-Gradient Method
  • 4.9. Systems of Differential Equations
  • 4.10. Eigenvalue Problem
  • 4.11. Inverse Power Method
  • 4.12. Problems
  • 5. Finite Element Method
  • 5.0. Introduction
  • 5.1. Galerkin Method
  • 5.2. Example Using Piecewise Linear Trial Functions
  • 5.3. Example Using Cubic Hermite Trial Functions
  • 5.4. Singular Example and The Collocation Method
  • 5.5. Linear Triangular Elements
  • 5.6. Example Using Triangular Elements
  • 5.7. Time-Dependent Problems
  • 5.8. One-Dimensional Example
  • 5.9. Time-Dependent Example Using Triangles
  • 5.10. Eigenvalue Problem
  • 5.11. Eigenvalue Examples
  • 5.12. Problems
  • Appendix A Solving PDEs with PDE2D
  • A.1. History
  • A.2. PDE2D Interactive and Graphical User Interfaces
  • A.3. One-Dimensional Steady-State Problems
  • A.4. Two-Dimensional Steady-State Problems
  • A.5. Three-Dimensional Steady-State Problems
  • A.6. Nonrectangular 3D Regions
  • A.7. Time-Dependent Problems
  • A.8. Eigenvalue Problems
  • A.9. PDE2D Parallel Linear System Solvers
  • A.10. Examples
  • A.11. Problems
  • Appendix B Fourier Stability Method
  • Appendix C MATLAB Programs
  • Appendix D Answers to Selected Exercises.

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