Abstract
In this chapter, we obtain results on the convergence of solutions to finite-difference approximations of boundary-value problems. More specifically, we study the convergence of finite-difference approximations to both linear and nonlinear ordinary differential equations of second order and to Poisson’s equation on a rectangle. In Chapter 1, appropriate finite-difference approximations were introduced, and both the exact and the approximate equations were expressed as operator equations. In addition, consistency of these methods (in the sense of Section 6.3) has been shown by an analysis of the truncation errors derived in Chapter 1.
Keywords
- Maximum Principle
- Convergence Analysis
- Truncation Error
- Nonlinear Ordinary Differential Equation
- Null Sequence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References (cf. also References in Chapter 1)
Bohl (1981), Ciarlet (1970)*, Courant & Hilbert (1966), Dorr (1970)*, Garabedian (1964), Grigorieff (1973b), Isaacson & Keller (1966), Keller (1968,1976), Mitchell (1969), Mitchell & Griffiths (1980), Vainikko (1976).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
Reinhardt, HJ. (1985). Convergence of Finite-Difference Methods for Boundary-Value Problems. In: Analysis of Approximation Methods for Differential and Integral Equations. Applied Mathematical Sciences, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1080-1_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1080-1_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96214-6
Online ISBN: 978-1-4612-1080-1
eBook Packages: Springer Book Archive