By Bichowsky F.R., Urey H.C.
Read or Download A Possible Explanation of the Relativity Doublets and Anomalous Zeeman Effect by Means of a Magnetic Electron PDF
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Additional resources for A Possible Explanation of the Relativity Doublets and Anomalous Zeeman Effect by Means of a Magnetic Electron
79335 91213. 1 Extrapolation to Zero Cell Size 15 h4 . 79335 91202. 79335 912. 05. This gives eight-digit accuracy of the extrapolation even though the computed data has only three to four correct digits. Thus, extrapolation can bring very signiﬁcant improvements of accuracy. Another advantage of extrapolation is that it makes us aware of how good the accuracy is. The example shows that good accuracy can also be obtained by using the higher-order Simpson integration, even without extrapolation, on a grid of moderate size.
4, even though the correct solution varies slowly on the scale of the grid. 16) such spurious solutions do not occur (however, the behavior is not entirely physical for this representation either when kh → π). 5 0 1 2 3 4 5 x/h [−] Fig. 4. Fastest oscillating function on a ﬁnite diﬀerence grid with kh = π has the derivative equal to zero at all integer points on the grid. 3) for the ﬁrst derivative gives an approximation with acceptable behavior even when kh = π. The derivative is computed on the half-grid, and the grids are staggered.
A simple method to estimate the error of a given computation is to (i) do a convergence test by uniform grid reﬁnement, (ii) ﬁnd the order of convergence, and (iii) extrapolate the computed results to zero cell size. • The order of convergence depend on the method and the regularity of the solution. Singular behavior of the solution decreases the order of convergence p in many real-world problems. 3) under the assumption that the integrand is regular. How does a singular integrand inﬂuence your derivation?
A Possible Explanation of the Relativity Doublets and Anomalous Zeeman Effect by Means of a Magnetic Electron by Bichowsky F.R., Urey H.C.