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Note that the built-in low order methods of MATLAB are used to obtain these results (Figure 2). Figure 2 Solutions of the deterministic model.
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In this paper, we present an embedded eighth order method of this type.
The algorithm implemented in this macro is similar to the first order method of Sheiner & Beal (1985).
The high order method of classes, developed in our earlier work [Alopaeus, V., Laakkonen, M., Aittamaa J., 2006a.
Second order method of multiple scales has been used to study the stability of the system for simply supported and clamped free sandwich beams.
Second order mUseiple-scales approfimathens, determined by using two different time co-ordinates, are compared.
In contrast with the DL estimator, which is derived as a 1st order method of moments estimator, the HM estimator is a 2nd order method of moments based estimator and has the following expression (7) σ H M 2 = Q (2 k − 1 + Q S 1 − S 2 / S 1 The HM estimator is consistently positive and has been shown to yield accurate and precise estimates of the between-trial variance [ 7, 9, 23].
The second group of methods presented in the paper refers to the general second-order methods of analysis.
This is the case of high order methods, examples of which are the p-version of the finite element method and the spectral element method.
Therefore, using this method, the parameters were adjusted in this order (Methods: Optimization of parameters).
A general high-order method of classes framework for numerical solution of population balances is developed and tested.
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