Linked Questions

5
votes
3answers
2k views

Plotting heat equation in a Manipulate expression [duplicate]

I have a 2D heat equation $u_t = \alpha (u_{xx} + u_{yy})$ with conditions: $u(x, y, 0) = 300$, $u_y(x, 0, t) = \mu_1(x)$, $u_y(x, 1, t) = \mu_2(x)$, $u(0, y, t) = \mu_3(y)$, $u(1, y, t) = \mu_4(y)$, ...
5
votes
1answer
442 views

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 ...
0
votes
0answers
68 views

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. ...
0
votes
0answers
58 views

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 ...
0
votes
0answers
53 views

Heat transport with Neumann bc in older Mathematica versions [duplicate]

Im trying to solve a simple heat transfer equation: $\partial_t T-\beta \partial_{xx}T=0$ for a finite system $x\epsilon <0;L>$ along with initial/boundary conditions: 1) $T(x,t)=0$ for $t<...
0
votes
0answers
33 views

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 ...
1
vote
0answers
18 views

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 ...
19
votes
1answer
996 views

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 ...
11
votes
1answer
1k views

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 \...
13
votes
1answer
1k views

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 ...
12
votes
1answer
620 views

Why does NDSolve fail to solve the PDEs and spit out mconly warning?

I try to solve two coupled PDEs with NDSolve using the following code: Set two operators: ...
8
votes
1answer
396 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 ...
4
votes
3answers
2k views

Solving a PDE containing DiracDelta

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(\...
4
votes
2answers
2k views

2d heat conduction equation: Boundary and initial conditions are inconsistent

I have the following code for a 2d heat c equation: ...
2
votes
2answers
306 views

Unstable solution of 2D+1 time PDE with periodic boundary condition

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)...

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