ABSTRACT

A source identification algorithm for systems of nonlinear ordinary differential equations of production-destruction type is applied to an inverse problem for a discretized Smoluchowski equation. An unknown source function is estimated by time series of measurements of particle concentrations of a specific size. Based on an ensemble of adjoint equation solutions, a sensitivity operator is constructed that relates perturbations of the sought-for model parameters with perturbations of the measured values. This reduces the inverse problem to a family of quasilinear operator equations. To solve the equations, an algorithm of the Newton–Kantorovich type with \(r\)-pseudoinverse matrices is used. The efficiency and properties of the algorithm are studied numerically.

中文翻译：

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使用伴随方程组解的Smoluchowski方程源识别

摘要

将生产破坏型非线性常微分方程组的源识别算法应用于离散Smoluchowski方程的反问题。通过特定尺寸颗粒浓度测量的时间序列来估算未知源函数。基于一组伴随方程解，构造了一个灵敏度算子，该算子将所需模型参数的扰动与测量值的扰动相关联。这将反问题简化为一系列拟线性算子方程。为了求解方程，使用了具有\（r \）-伪逆矩阵的Newton–Kantorovich类型的算法。对算法的效率和性质进行了数值研究。