H 2h algorithm

In Figure 11.5 the error varies essentially as h as can be seen by the factor of 16 difference between the upper and lower curves in the figure. This is to be expected from the extensive discussion in Chapter 10 on the accuracy of the TP algorithm for initial value problems. This means that a good estimate of the error in file solution can be obtained by use of the h-2h algorithm discussed in the previous... 

Figure 12.6. Comparison of exact error for diffusion equation with error estimate based upon the h-2h algorithm. Curves are very close near the peak errors for each solution.

Figure 12.11. Estimated error in solutions for the tubular chemical reactor obtained by the h-2h algorithm at t = 20. Solid lines are solutions. Dotted curves are estimated errors.

Listing 12.35. Code for estimating error of PDE solution by h-2h algorithm. 

Figure 12.86. Surface plot of error around p-n junction obtained by the h-2h algorithm.

---