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American cardinals who voted in the conclave played down the significance of the new pope’s roots in the United States, saying his service to the poor and the church had propelled him to the papacy.

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 ...

Abstract: We consider first-order linear systems of ordinary differential equations with periodic boundary conditions and unknown right-hand sides which are subjected to some quadratic restrictions.

Riccati equations are a natural next step after you’ve studied linear differential equations. Linear first-order ordinary differential equations look like this: I think I finally get why they’re ...

Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical ...