Section 1. Purpose. United States leadership in Artificial Intelligence (AI) will promote United States national and economic security and dominance across many domains. Pursuant to Executive Order ...
Abstract: We apply first- and second-order splitting schemes to the differential Riccati equation. Such equations are very important in, e.g., linear quadratic regulator (LQR) problems, where they ...
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 ...
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 ...
This paper addresses the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics by introducing a novel framework called ...
The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both ...
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 ...
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