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### Plotting heat equation in a Manipulate expression [duplicate]

I have a 2D heat equation $u_t = \alpha (u_{xx} + u_{yy})$ with conditions: $u(x, y, 0) = 300$, $u_y(x, 0, t) = \mu_1(x)$, $u_y(x, 1, t) = \mu_2(x)$, $u(0, y, t) = \mu_3(y)$, $u(1, y, t) = \mu_4(y)$, ...
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### Incorrect results of diffusion equation with Neumann boundary conditions [duplicate]

I want to resolve a PDE model, which is 1D heat diffusion equation with Neumann boundary conditions. The key problem is that I have some trouble in solving the equation numerically. Consider the ...
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### Why DSolve and NDSolve give different answer? [duplicate]

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? I'm using version 11.0 on Windows 8.1. ...
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### Are the following Mathematica codes correct for solving wave equation PDE? [duplicate]

I wanna solve the following PDE of wave equation using Mathematica. $u_{tt}=u_{xx}$ $0<x<\pi , t>0$ Initial Conditions: $\begin{cases}u(x,0)=sin(x) \\u_{t}(x,0)=1\end{cases}$ Boundary ...
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### NDSolve is not always easy to handle [duplicate]

I solve the PDE system analytically and numerically and get totally different results. Should there be a solution to the problem of the numerical solution, one must ask oneself - do you know the ...
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### Initial condition true everywhere but on a boundary, when NDSolving with a TensorProductGrid discretization [duplicate]

I am now focusing on using NDSolve with the method of lines and the TensorProductGrid spatial discretization to integrate PDEs. My problem is to integrate the wave equation from t=0 to t=2 with an ...
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### Couple a PDE and ODE in NDSolve

I would like to solve an example of non-stationary heat transfer with a coupled PDE and ODE. Let's assume that we have 1 dimensional bar of length $L$ with uniform initial temperature. The right end ...
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### Differences between DSolve and NDSolve

I have a question about the difference in the solution between DSolve and NDSolve. I want to solve the Friedmann equation of \...
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### NDSolveValue - Heat flux continuity

I'm having some problems with NDSolve and the problem of conduction of heat. Specifically I'm having problems with the continuity of heat flux. First, let me ...
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### Why does NDSolve fail to solve the PDEs?

I try to solve two coupled PDEs with NDSolve using the following code: Set two operators: ...
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I want to get the answer from a PDE: \begin{align*} \frac{\partial \rho(r,t)}{\partial t}&=Dr^{-2}\frac{\partial}{\partial r}r^2h(r)e^{-U(r)}\frac{\partial}{\partial r}e^{U(r)}\rho(r,t)-\left(\... 2answers 1k views ### 2d heat conduction equation: Boundary and initial conditions are inconsistent I have the following code for a 2d heat c equation: ... 1answer 302 views ### How to solve a system of PDEs with zip condition? I have a system of PDEs in the following form,\frac{\partial T_1}{\partial t}=\frac{\partial^2 T_1}{\partial x^2},\,\,0<x<S(t) with $T_1(x,0)=-10,\,\,T_1(0,t)=-10,\,\, T_1(S(t),t)=10$, and ...
According to the documentation about the pseudospectral difference-order: It says: Following the discussion here: I found the messy behavior is always on the artificial boundary in $\omega$-...
Now I am trying to solve the following 2D+1 type of PDE: $\partial_t u(t,x,y)=-y\partial_{x}u+\partial_{y}\left[a y+b sin(x)u+c\partial_{y}u\right]$ with \$u(0,x,y)=\frac{1}{2\pi}e^{-((x-\pi/4)^2+y^2)...