求解反应动力学参数的一类方法

A kind of method for solving reactive kinetic parameters

反应动力学实验中得到的数据误差较大,且分布不均匀.因此,在处理反应动力学数据时,采用插值法拟合要求通过每个数据点,因数据误差较大,必然会引起震荡;而采用多项式拟合要求提前选定拟合函数,当所选函数与实际函数存在较大误差时,甚至会导致对实际化学意义的违反.针对这一问题,本文提出了一种采用自然三次样条插值求解反应动力学参数的方法.这种方法充分利用所得数据和化学反应方程组自身隐含的数学性质,不但保证了对原始数据的逼近,而且保证了所得函数为二阶光滑,避免了震荡的出现,取得了较好的拟合效果;并且为Runge-Kutta迭代方法提供了一个较好的初值,加快了算法的收敛.该方法特别适用于实验数据误差较大且数据点较少的情况.

The data obtained in reactive kinetic experiments usually include evident experimental errors and have nonuniform distribution.In processing the data,interpolation fitting method require fitting curve to cross all the data points,therefore the greater vibration of the curve is certainly caused because of the greater errors of the data;polynomial approximation must determinate fitting function in advance,the violation of practical chemical meaning may be caused if there is greater difference between the selected function and real function.For solving the problem,a kind of the method for solving reactive kinetic parameters is put forward which makes use of natural cubic spline interpolation.The method makes full use of the mathematical properties of the data and reaction equations,which not only ensures the approximation to the data but it is sure that the obtained function is quadratically smooth.Therefore,the method has better matched result.It also provides a better initial value for Runge-Kutta iteration method and accelerates the convergence of the algorithm.The method is specially suitable for less experimental data and the data with greater experimental errors.