Convergence of Finite-Difference Methods for Boundary-Value Problems
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.
KeywordsMaximum Principle Convergence Analysis Truncation Error Nonlinear Ordinary Differential Equation Null Sequence
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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).Google Scholar