The results presented in figure 352 compare the base

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Unformatted text preview: andPrince method was designed for this purpose. For this problem, which has a smooth ; ; 53 Figure 3.5.2: Accuracy vs. e ort for several explicit Runge-Kutta methods 16]. 54 solution, the Dormand-Prince method is nearly a factor of 10 more accurate with local extrapolation than without it. Numerous other implementation details have not been addressed. These include (i) Newton iteration for implicit systems and (ii) portability. We will return to these topics when discussing multistep methods in Chapter 5. While we have not discussed competing methods, we'll nevertheless conclude that explicit Runge-Kutta formulas should be considered when 1. the functions de ning the di erential system are simple or 2. the solution has discontinuities. The latter case is interesting. Discontinuities can be ignored and treated with the automatic step-size selection procedures. This is easier to do with Runge-Kutta methods than with competing approaches such as multistep methods. Explicit treatment of discontinuities b...
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