## Abstract

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.

Original language | English |
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Pages (from-to) | 51-69 |

Number of pages | 19 |

Journal | Numerical Analysis and Applications |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

## Keywords

- adjoint equations
- big data
- inverse source problem
- Newton–Kantorovich method
- r-pseudoinverse matrix
- right inverse
- sensitivity operator