Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Matrix Methods
- Part II Numerical Methods
- 6 Computational Linear Algebra
- 7 Numerical Methods for Differential Equations
- 8 Finite-Difference Methods for Boundary-Value Problems
- 9 Finite-Difference Methods for Initial-Value Problems
- Part III Least Squares and Optimization
- References
- Index
8 - Finite-Difference Methods for Boundary-Value Problems
from Part II - Numerical Methods
Published online by Cambridge University Press: 18 February 2021
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Matrix Methods
- Part II Numerical Methods
- 6 Computational Linear Algebra
- 7 Numerical Methods for Differential Equations
- 8 Finite-Difference Methods for Boundary-Value Problems
- 9 Finite-Difference Methods for Initial-Value Problems
- Part III Least Squares and Optimization
- References
- Index
Summary
The application of finite-difference methods to boundary-value problems is considered using the Poisson equation as a model problem.Direct and iterative methods are given that are effective for solving elliptic partial differential equations in multidimensions having various types of boundary conditions.Multigrid methods are given particular attention given their generality and efficiency.Treatment of nonlinear terms are illustrated using Picard and Newton linearization.
Keywords
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2021