Error tmncation

Other moments of momentum can also be obtained directly from the Compton profile without first going through the numerical differentiation of Eq. (40) which is prone to roundoff and tmncation errors. Several groups [55,67-70] independently reported one or more of the sum rules... 

We want to mention here that the application of the near-nuclear corrections could have been performed with the complete relativistic functional, and we have utilized the semi-relativistic expressions just for simplicity and for testing them. For not large Z, the remaining errors above mentioned should be addressed to hmitations of the semiclassical approach and of the procedure utilized for the near-nuclear corrections, rather than to the tmncation of the expansion in powers of c... 

The major computational effort in applying the Rxmge-Kutta methods occurs in the evaluation of /. For second-order methods, two functional evaluations per step are required, and for the fourth-order method, four evaluations per step are required. As a consequence, the lower-order methods with smaller step size may be less costly than the higher-order methods using a larger step size. Relationships between evaluations per step and the order of local tmncation error can be found in the literature [24]. Also available in the numerical analysis literature [15] are developments that combine the best features of the Euler and a second-order Runge-Kutta method. 

Truncation error results from using a function like a polynomial to approximate the true solution. To reduce tmncation error, we could use more sophisticated functions—for example, higher order polynomials—which require more information. Multistep methods do this, but the additional accuracy gained by increasing the order of the method drops off very quickly beyond about k = 4. 

An important aspect of Eulerian reactor models is the tmncation errors caused by the numerical approximation of the convection/advection terms [96], Very different numerical properties are built into the various schemes proposed for solving these operators. The numerical schemes chosen for a particular problem must be consistent with and reflect the actual physics represented by the model equations. 

Comparing (12.107) and (12.113), it is seen that the leading tmncation error term in CDS is proportional to the square of the grid spacing, hence the central difference scheme is second order accurate both on uniform and non-uniform grids. 

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