Error coefficients

From the final value theorem given in equation (3.10) it is possible to define a set of steady-state error coefficients. 

This equation applies to vaporization of single components, but can be used for close boiling mixtures without too much error. Coefficients for wide boiling mixtures will be overestimated. 

Coefficient of determination for a given training set standard error coefficient of determination for a given test set F-value number of observations and neural network. 

Term Coefficients Standard error coefficient T-test value P-Value... 

Another, even more drastic approximation was proposed by Wilhite and Euwema. In this method, the entire charge distribution function (which is the product of two contracted Gaussians) is replaced by a few s-type Gaussian functions. To minimize the error, coefficients and exponents of the replacement functions are calculated by equating the magnitudes of several multipole moments of the original and approximate charge distributions. 

In [211] the authors obtained a new embedded 4(3) pair explicit four-stage fourth-order Runge-Kutta-Nystrom (RKN) method to integrate second-order differential equations with oscillating solutions. The proposed method has high phase-lag order with small principal local truncation error coefficient. The authors given the stability analysis of the proposed method. Numerical comparisons of this new obtained method to problems with oscillating and/or periodical behavior of the solution show the efficiency of the method. 

The existence of this expansion is hard to prove theoretically but easy to monitor within the adaptive algorithm. Solving the problem with different internal time stepsizes Atj = ATfjyj = ,..., and two nested space grids (Ari = AR, Av2 = AR/2) allows to eliminate the leading error coefficients by a coupled extrapolation in space and time. This extraploation... 

In response, the model should be able to draw the theoretical curve which fits the experimental data better, and give the diffusion parameters obtained for this fitting, the diffusivity and the coefficient of convection, as well as the error coefficient evaluating the accuracy of these values as high as possible. 

Standard error Coefficient of determination Variance ratio (F test)... 

The further evaluation of these two options is treated elsewhere (13). The error coefficient matrix of eq 20 has now become meaningless, and so the standard deviation of the fit (eq 21), since these are only valid when having equal variances V for all the measurements. The variances are not equal anymore, since the zero charge condition will have another variance than the actual conductivity measurements. 

Balance the formula equation according to the law of conservation of mass. This last step is done by trial and error. Coefficients are changed and the numbers of atoms are counted on both sides of the equation. When the numbers of each type of atom are the same for both the products and the reactants, the equation is balanced. The trial-and-error method of balancing equations is made easier by the use of the following guidelines. 

The implicit multistep methods add stability but require more computation to evaluate the implicit part. In addition, the error coefficient of the Adams-Moulton method of order k is smaller than that of the Adams Bashforth method of the same order. As a consequence, the implicit methods should give improved accuracy. In fact, the error coefficient for the imphcit fourth-order Adams Moulton method is 19/720, and for the explicit fourth-order Adams Bashforth method it is 251/720. The difference is thus about an order of magnitude. Pairs of exphcit and implicit multistep methods of the same order are therefore often used as predictor-corrector pairs. In this case, the explicit method is used to calculate the solution,, at v +i. Furthermore, the imphcit method (corrector) uses y + to calculate /(x +i,y +i), which replaces /(x +i,y +i). This allows the solution, y +i, to be improved using the implicit method. The combination of the Adams Bashforth and the Adams Moulton methods as predictor orrector pairs is implemented in some ODE solvers. The Matlab odel 13 solver is an example of a variable-order Adams Bashforth Moulton multistep solver. 

---