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.1007/BF01203463 . [11] Lubinsky , D. S. , Sidi , A. 2007 Biorthogonal polynomials and numerical integration formulas for infinite ntervals J. Num. Analysis, Industrial and Appl. Math. 2 1

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carried out by comparison of experimental conversion curves α exp ( T ) with the α clc ( T ) values calculated by numerical integration of dα clc ( T )/d T values within the conversion range α ⊂ 〈0.05;0.95〉. Values of dα clc ( T )/d T were calculated

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.e. unweighted) least-squares regression, yields the values of k , T ∞ , T ini,e and T fin,s . Then the data of the main period, {( t i , T i ), t ini,e ≤ t i ≤ t fin,s }, are evaluated by numerical integration, to compute an approximate value of the

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.81 Continuing, from experimental curves α − T , the term dα/d T could be determined by numerical integration. Thus, the data dα/d T plus activation energy from Table 3 could be substituted in the right side of Eq. 3 to obtain the experimental f (α) g (α

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Journal of Thermal Analysis and Calorimetry
Authors: Rogério L. Pagano, Verônica M. A. Calado, Frederico W. Tavares, and Evaristo C. Biscaia

correspondent confidence regions for the estimated parameters. The ultimate reaction heat, obtained by numerical integration of the reaction heating rate conducted isothermically in DSC experiments, lies outside the confidence region of the reaction heat

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Reaction Kinetics, Mechanisms and Catalysis
Authors: Saet Byul Kim, Mi Ran Lee, Eun Duck Park, Sang Min Lee, HyoKyu Lee, Ki Hyun Park, and Myung-June Park

subroutine in MATLAB™ (The MathWorks, Inc.) where the Levenberg–Marquardt method is applied. The numerical integration of Eqs. 7 and 8 , required during each iterative step in the nonlinear regression, was performed by the ODE solver, ode23s in MATLAB

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Journal of Thermal Analysis and Calorimetry
Authors: Hernani S. Barud, Clóvis A. Ribeiro, Jorge M. V. Capela, Marisa S. Crespi, Sidney. J. L. Ribeiro, and Younes Messadeq

numerical integration. Thus, the d α/ d T data plus the activation energy from Table 2 could be substituted in the right side of Eq. 3 to obtain the experimental f ( α ) g ( α ) for each heating rate against α , Fig. 6 , and then compared with the

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: (10) The parameters could be evaluated by numerically integrating the kinetic equations using a fourth-order Runge–Kutta method, by minimizing the F between the calculated and experimental data: Supposing the reaction is controlled by a different

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is the pressure in atm, T is the absolute temperature; B 1 , C 1 are the Antoine coefficients. The parameter Δ 12 is calculated using the second virial coefficients from the equation: 12 The Eq. 9 is solved by numerical integration

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− M -1   K       0 ]     ,     b u = [ 0 − M − 1   f t ]     , and I is a unit matrix. Numerical integration of (32) can be performed with number of standard methods, e.g. Runge-Kutta method or trapezoid rule, using Matlab or Scilab software

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