Abstract
This chapter elaborates the stability of the ordinary differential approximations. It is straightforward to determine if a finite difference scheme is stable. It is found that if a finite difference scheme is stable, then a locally good approximation yields a globally good approximation. Difference schemes for ordinary differential equations may be stable, or unstable. The definition closely parallels the definition for the stability, and well-posedness of a differential equation. A stable difference scheme is one in which small changes in the initial, and boundary data do not change the solution greatly. An unstable difference scheme is one that shows great sensitivity to the initial, and boundary data.
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