中文摘要：

在采用泰勒分散法测量多元体系溶液的分子扩散系数的实验中，实验过程的数理模型包含多个待求参数，且需从多条符合同一个方程的实验曲线中提取出所需的实验结果。这是一个多曲线多参数的非线性拟合问题。基于最小二乘法建立了求解模型，采用 Gauss-Newton 法对模型中的参数进行不断逼近。通过2组（每组有5条曲线）由计算机生成的虚拟曲线对基于Gauss-Newton法的Matlab程序进行检验，结果表明：在所得的8个分子扩散系数中，Gauss-Newton法处理结果与真实值的平均相对偏差为3.18%，最大相对偏差为8.67%。

英文摘要：

In order to obtain the results of multi-component Taylor dispersion experiment, it needs to fit more than two measurement curves to the same function, in which contains the needed diffusion coefficients. It is a nonlinear fitting problem about multi-curves and multi-parameters. A mathematical model have been built based upon the least-square-method. The Gauss-Newton method has been used to gradually approach the parameters in the model. The reliability of the MATLAB code, based on the Gauss-Newton method, has been checked by three sets of simulation curves. Results show that, the fitting results adequately agreed with the simulation values, with the average relative error of 3.18%and the maximum relative error of 8.67%.