## Abstract

A source identification algorithm for systems of nonlinear ordinarydifferential equations of production-destruction type is applied to aninverse problem for a discretized Smoluchowski equation. An unknownsource function is estimated by time series of measurements of particleconcentrations of a specific size. Based on an ensemble of adjointequation solutions, a sensitivity operator is constructed that relatesperturbations of the sought-for model parameters with perturbations ofthe measured values. This reduces the inverse problem to a family ofquasilinear operator equations. To solve the equations, an algorithm ofthe Newton–Kantorovich type with r-pseudoinversematrices is used. The efficiency and properties of the algorithm arestudied numerically.

Original language | English |
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Pages (from-to) | 152-164 |

Number of pages | 13 |

Journal | Numerical Analysis and Applications |

Volume | 13 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 2020 |

## Keywords

- adjoint equations
- inverse source problem
- Newton--Kantorovich method
- sensitivity operator
- Smoluchowski equation