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### How does Return work?

It is not completely clear to me how Return[] works. The documentation says: Return[expr] returns the value expr from a ...
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### Reduce ODE into 1st order

I have an explicit set of differential equations: $\ddot{x}=f(x,\dot{x})$ I would like to reduce it in the following way: $\dot{y} = g(y)$ by substitutions as shown here: wikipedia. I have done ...
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### Solving an integro-differential equation with Mathematica

I try to solve a nonlinear integro-differential equation with this code. Here i used a periodic condition. ...
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### PDE of real-world system, integral boundary condition

I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ...
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### System of PDE with integration conditions interior of domain

I am trying to solve this system of pde numerically. I am unable to find any method in Mathematica that can handle this problem. The issue is having this integration condition in the domain. I tried ...
• 103
I have a set of pdes in 2D space and 1D time, one of them is related to the integral in space by Reynolds function. The equations are similar to \frac{\partial \phi}{\partial t}=-\frac{\partial \...