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 ...

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 ...

Progress Check: We’re now about 23% of the way through the season, and Memorial Day – a day people say standings start to matter – is 18 days away. The point has come where we can’t simply dismiss 6 ...

The Associated Press accused the White House of violating a court order after it was once again banned from an Oval Office event. On Monday, AP writer David Bauder reported that a reporter and ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

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 ...

In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the ...

Can Weak SINDY be used on higher order ordinary differential equations, for example the van der Pol equation (a second order differential equation): x''(t) - mu (1-x^2) x' + x = 0 (where x' is the ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

The object of this work is to describe how to implement the differential ‎transformation method (DTM) for finding exact and approximate solutions of ‎the second-order random differential equations. To ...