Algorithms for solving an inverse source problem for production–destruction systems of nonlinear ordinary differential equations with measurement data in the form of time series are presented. A sensitivity operator and its discrete analogue are constructed on the basis of adjoint equations. This operator relates perturbations of the sought-for parameters of the model to those of the measured values. The operator generates a family of quasi-linear operator equations linking the required unknown parameters and the data of the inverse problem. A Newton–Kantorovich method with right-hand side r-pseudo-inverse matrices is used to solve the equations. The algorithm is applied to solving an inverse source problem for an atmospheric pollution transformation model.

中文翻译：

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时间序列类型测量数据的生产-破坏模型逆源问题的牛顿-坎托罗维奇方法

提出了求解时间序列形式的测量数据的非线性常微分方程生产-破坏系统的逆源问题的算法。灵敏度算子及其离散类似物是在伴随方程的基础上构造的。该运算符将模型的所需参数的扰动与测量值的扰动联系起来。算子生成一系列准线性算子方程，这些方程将所需的未知参数与反问题的数据联系起来。带有右侧r-伪逆矩阵的Newton-Kantorovich方法用于求解方程。该算法用于求解大气污染转化模型的逆源问题。