Comparative Analysis of Gradient Methods for Source Identification in a Diffusion-Logistic Model

• Published in: Computational mathematics and mathematical physics Vol. 62; no. 4; pp. 674 - 684
• Main Authors: Zvonareva, T. A., Krivorot’ko, O. I.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2022; Springer Nature B.V
• Subjects: Comparative analysis; Computational Mathematics and Numerical Analysis; Computing time; Diffusion; Discrete functions; Information dissemination; Logistics; Mathematical models; Mathematical Physics; Mathematics; Mathematics and Statistics; Social networks; Spline functions; inverse problem; comparative analysis; diffusion-logistic model; optimization; regularization; adjoint problem; gradient methods; social processes; source identification problem
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542522040145

The paper presents a comparative analysis of the numerical solution of the problem of source identification in the diffusion-logistics model from the data on the diffusion process at fixed points in time and space by gradient methods in continuous and discrete formulations. Expressions are obtained for calculating the gradient of the objective functional for two formulations related to the solution of the corresponding adjoint problems. It is shown that, if the discrete functions of the model are approximated by cubic splines, the accuracy of the solutions of the source identification problem has the same order in the case of continuous and discrete calculation of the gradient. Numerical experiments in solving the source identification problem for a discrete model of information dissemination in online social networks have shown that the use of the discrete approach significantly increases the computational time in comparison with the continuous approach.