Error Propagation, Stability, and Convergence

The truncation and roundoff errors in numerical integration accumulate and propagate, creating the propagation error, which, in some cases, may grow in exponential or oscillatory pattern, thus causing the calculated solution to deviate drastically from the correct solution. 

Error propagation in numerical integration methods is a complex operation that depends on several factors. Roundoff error, which contributes to propagation error, is entirely determined by the accuracy of the computer being used. The truncation error is fixed by the 

Numerical Solution of Ordinary Differential Equations Chapters 

In the sections that follow, we examine systematically the error propagation and stability of several numerical integration methods and suggest ways of reducing these errors by the appropriate choice of step size and integration algorithm. 

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