Inverse problems in differential equations constitute a pivotal area in applied mathematics and engineering, where the aim is to deduce unknown parameters or inputs within a differential equation from ...

Abstract: Curved spaces, such as surfaces, provide a rich setting for the study of partial differential equations (PDEs). Building upon the extensive research conducted on PDEs in flat spaces, the ...

Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun, Turkey. Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun, Turkey. In ...

Inverse problems, central to modern applied mathematics, involve deducing unknown parameters or functions in differential equations from observed spectral data. This field is pivotal in understanding ...

Abstract: Many scientific and real-world problems that occur in science, engineering, and medicine can be represented in differential equations. There is a vital role for differential equations in ...

The radiative transfer phenomenon is modeled by an integro-differential equation known as Boltzmann equation. This equation describes mathematically the interaction of the radiation with the ...

In this paper we present a hybrid approach to numerically solving two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous ...

We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a ...

Codes associated with the manuscript titled "Subspace method based on neural networks for solving the partial differential equation" authored by Zhaodong Xu and Zhiqiang Sheng. This repository ...