Abstract: Physics-informed neural networks (PINNs) offer a flexible framework for solving differential equations using physical constraints and data. This study focuses on second-order ...

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Abstract: Recently, variational and partial differential equation (PDE)-based algorithms have become very important for image restoration. In this study, we propose a new second order hyperbolic PDE ...

This paper addresses the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics by introducing a novel framework called ...

1 Department of Thoracic Surgery, The First Medical Centre, Chinese PLA General Hospital, Beijing, China 2 Medical School of Chinese PLA, Beijing, China We address mathematical modelling of ...

Phenomena such as mechanical vibrations, resonance and oscillations can be mathematically described by second-order differential equation systems, commonly referred to as second-order systems. Working ...

In geometrically nonlinear problems solved using the Finite Element Method (FEM), the structure response is directly influenced by the level of discretization and the nonlinear solution algorithm used ...

In this paper, the boundary value problems for second order singularly perturbed delay differential equations are treated. A generic numerical approach based on finite difference is presented to solve ...