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Test of the fractional_method C-function

The C-implementation of the fractional iteration method, the function fractional_method, was run with the super-critical test reactor. As previously, the eigenvalue estimate was obtained by running the power method with a convergence criterion of $\epsilon = 10^{-2}$ and with this estimate at hand the fractional iteration method was brought to convergence with an accuracy criterion of $\epsilon = 10^{-14}$. The calculated eigenvalue, $\lambda_{\mbox{\protect\scriptsize FI}}$, had the following value

$$\lambda_{0,{\mbox{\protect\scriptsize FI}}} = 1.0738684260100841$$ (4.16)

which is almost identical to the exact (Matlab calculated) value

$$\lambda_{0,{\mbox{\protect\scriptsize Matlab}}} = 1.073868426010085$$ (4.17)

The calculated eigenvector, $\hspace{0.2ex}\underline{\phi}{}\hspace{0.15ex}_{\mbox{\protect\scriptsize FI}}$, was compared to the one calculated by Matlab with the result

$$\Vert \hspace{0.2ex}\underline{\phi}{}\hspace{0.15ex}_{\mbo... ...otect\scriptsize Matlab}} \Vert _\infty = 1.021 \cdot 10^{-14}$$ (4.18)

Finally, the exact eigenvalue error, $E_{\lambda,k}$, defined by (4.10) is depicted in Figure 4.19. When this figure is compared to its Matlab counterpart Figure 4.15 the correctness of the C-function is confirmed.

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