Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...
Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...
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Abstract: Time-variant fractional systems have many applications. For example, they can be used for system identification of lithium-ion batteries. However, the analytical solution of the time-variant ...
We study the existence of positive solutions of the equation u״ (t) + a (t) f (u(g(t))) = 0, 0 < t < 1 with linear boundary conditions. We show the existence of at least one positive solution if f is ...
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 ...
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Abstract: We address forward–backward stochastic differential equations (FBSDEs) with random coefficients. Differently from previous approaches, we consider FBSDEs with coefficients that are random ...
The need to investigate functional differential equations with discontinuous delays is addressed in this book. Recording the work and findings of several scientists on differential equations with ...