Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Symbols
- Part I Numerical Linear Algebra
- Part II Constructive Approximation Theory
- Part III Nonlinear Equations and Optimization
- Part IV Initial Value Problems for Ordinary Differential Equations
- 17 Initial Value Problems for Ordinary Differential Equations
- 18 Single-Step Methods
- 19 Runge–Kutta Methods
- 20 Linear Multi-step Methods
- 21 Stiff Systems of Ordinary Differential Equations and Linear Stability
- 22 Galerkin Methods for Initial Value Problems
- Part V Boundary and Initial Boundary Value Problems
- Appendix A Linear Algebra Review
- Appendix B Basic Analysis Review
- Appendix C Banach Fixed Point Theorem
- Appendix D A (Petting) Zoo of Function Spaces
- References
- Index
18 - Single-Step Methods
from Part IV - Initial Value Problems for Ordinary Differential Equations
Published online by Cambridge University Press: 29 September 2022
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Symbols
- Part I Numerical Linear Algebra
- Part II Constructive Approximation Theory
- Part III Nonlinear Equations and Optimization
- Part IV Initial Value Problems for Ordinary Differential Equations
- 17 Initial Value Problems for Ordinary Differential Equations
- 18 Single-Step Methods
- 19 Runge–Kutta Methods
- 20 Linear Multi-step Methods
- 21 Stiff Systems of Ordinary Differential Equations and Linear Stability
- 22 Galerkin Methods for Initial Value Problems
- Part V Boundary and Initial Boundary Value Problems
- Appendix A Linear Algebra Review
- Appendix B Basic Analysis Review
- Appendix C Banach Fixed Point Theorem
- Appendix D A (Petting) Zoo of Function Spaces
- References
- Index
Summary
We present and analyze the simplest single step schemes for the approximation of the solution to an initial value problem: forward and bacward Euler, trapezoidal and midpoint rules, and Taylor’s method. We discuss the notions of consistency error and convergence for these schemes
Keywords
- Type
- Chapter
- Information
- Classical Numerical AnalysisA Comprehensive Course, pp. 525 - 535Publisher: Cambridge University PressPrint publication year: 2022