Integral transforms play a foundational role in applied mathematics, statistics, and theoretical physics, serving as powerful ...
Masaki Kashiwara has won the 2025 Abel prize, sometimes called the Nobel prize of mathematics, for his work on algebraic analysis. Kashiwara, a professor at Kyoto University, Japan, received the award ...
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Abstract: This paper introduces Physics-Informed Deep Equilibrium Models (PIDEQs) for solving initial value problems (IVPs) of ordinary differential equations (ODEs). Leveraging recent advancements in ...
Researchers have made a breakthrough in the ability to solve engineering problems. In a new paper published in Nature entitled, “A scalable framework for learning the geometry-dependent solution ...
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 ...
Have you ever wondered how complex phenomena like fluid flows, heat transfer, or even the formation of patterns in nature can be described mathematically? The answer lies in partial differential ...
From writing essays to coding, there’s seemingly nothing modern AI chatbots like ChatGPT and Microsoft Copilot cannot accomplish. But even though they seem limitless on the surface, they’re certainly ...
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