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### PDE with NDSolve gives solution despite not enough boundary conditions [duplicate]

For a given PDE, uniqueness of the solution requires boundary/initial conditions, the exact type of conditions depending on the particular PDE under consideration. For example consider the wave ...
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### Numerically solve the initial value problem for the 1-D wave equation

I want to solve the standard 1-dimensional wave equation $y_{xx}=y_{tt}$ using NDSolve (for $y(x,t)$) with the following conditions: ...
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### PDEs : automatic method choice : TensorProductGrid or FiniteElement?

A problem that arises when we solve PDEs with NDSolve[] and Method->Automatic is how to know which method has been chosen : <...
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### How to take derivative of the argument of an interpolating function

I am trying to plot the derivative of the argument of an interpolating function u[t, x] with respect to $x$. Here, u[t, x] is ...
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### How to modify a PDE inside NDSolve according to an if condition

I need to solve this PDE $$\partial_tf(t,x)+\partial_xf(t,x)+k\partial_{xx}f(t,x)-xf(t,x)=0$$ with $k\in\mathbb{R}$ and final condition $f(T,x)=1$ with $0<t<T$. My problem is how to solve ...
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### NDSolve: method of lines: unexpected error: insufficient boundary conditions

As a test of my ability to master the Method of Lines I tried to NDSolve the PDE's system \partial_t \varphi = \varpi\qquad\partial_t\varpi=\frac{1}{r}\partial^...
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### Singularity while solving PDE

I have to solve a PDE (in the context of the functional renormalization group in physics). I have a function of two variables, $U(l,p)$. I know $U(0,p)=U_0(p)$ and then I have an equation (eq925) that ...
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### Automatic Boundary conditions in NDSolve

I would like to know what kind of boundary conditions Mathematica implements in NDSolve when not specifying any boundary conditions by hand. So for example solving ...
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### Solve nonlinear coupled PDE with x,y and t dependent

I am trying solve the following two coupled PDE equations. ∂f/∂t=(∂^2 f)/(∂x^2 )+(∂^2 f)/(∂y^2 )-1/f^3 [(∂B/∂x)^2+(∂B/∂y)^2 ]-f+f^3 (∂^2 B)/(∂x^2 )+(∂^2 B)/(∂y^2 )-B*f^2+2/f [(∂B/∂x)(∂f/∂x)-(∂B/∂y)(...
I need to solve the following equation $\frac{\partial^2 \Phi}{\partial u^2}=\frac{\partial \Phi}{\partial u} \frac{\partial \Phi}{\partial \tau}$ with some initial condition $\Phi (u,0)$ to which the ...