Linked Questions

12 votes
3 answers

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 ...
Mirko Aveta's user avatar
  • 2,192
6 votes
3 answers

How to input Robin boundary conditions for nonstandard Laplace equation?

What is the correct way to input these boundary conditions for the following nonstandard Laplace equation, whose coefficients of $\frac{\partial^2 u}{\partial x^2}$ and $\frac{\partial^2 u}{\partial y^...
zhk's user avatar
  • 11.9k
12 votes
4 answers

Position of discontinuous coefficient influences the solution of PDE

This issue is raised in the discussion under this post about heat flux continuity and I think it's better to start a new question to state it in a clearer way. Just consider the following example: <...
xzczd's user avatar
  • 66.2k
8 votes
2 answers

DirichletCondition in NDSolve causes asymmetry (Finite Element Method)

Edit Thanks for the responses. I now agree with xzczd and Bill Watts who kindly gave answers and user21 who wrote useful comments. Both my cases below are correct. On reflection I think I made an ...
Hugh's user avatar
  • 16.5k
3 votes
1 answer

How to solve fourth order differential equation?

I have a differential equation of this type: y[x] - 1 - 2*l^2*y''[x] + l^4*y''''[x] == 0 (where l is a parameter and ...
Cro Simpson2.0's user avatar
2 votes
2 answers

What causes the warning "The dependent variable in the boundary condition needs to be linear" when using NDSolve?

V 12.1.1 on windows 10 Why the following works ...
Nasser's user avatar
  • 144k
7 votes
1 answer

1D-waveequation with absorbing boundary condition: FEM solution?

I try to simulate the special absorbing(?) boundary condition `Derivative[1, 0][y][1, t] + Derivative[0, 1 ][y][1, t] == 0` which only allows energy flow in ...
Ulrich Neumann's user avatar
3 votes
1 answer

NDSolve 1D Heat equation with NeumannValue poorly satisfies boundary condition

Context I am trying to measure the slope of the stellar cuspide around our MilkyWay's central black hole using the observed distribution of S stars orbiting around it. Attempt Close to the ...
chris's user avatar
  • 23k
5 votes
1 answer

Problem with using NDSolve on wave PDE on string

I am trying to verify my hand solution for wave PDE in 1D, on a string. The solution I get from NDSolve does not match the analytical solution. This is a string, ...
Nasser's user avatar
  • 144k
2 votes
1 answer

How to solve Neumann boundary ODE with shooting method?

$\rho(x)$ is the distribution function. I'm trying to solve the following equation: $D_t\frac{\partial^2\rho}{\partial x^2}-\frac{\partial (v_0\rho)}{\partial x}=0$ $D_t\frac{\partial\rho}{\partial x}-...
江蛮子's user avatar
2 votes
0 answers

NDSolve gives different result if I use NeumannValue to set initial condition

While trying to get familiar with the NeumannValue function I tried solving the wave equation on $r\in [0,2\pi]$ for $\theta(t,r)$ $$\partial^2_t \theta - \partial^2_r \theta =0, $$ with intial ...
Rudyard's user avatar
  • 471
0 votes
0 answers

Using NeumannValue in finite element method to replace a derivative boundary condition in NDSolve to overcome a computational overflow

I am trying to implement and evaluate the function GeneratePsiOfX. The definition of GeneratePsiOfX is: ...
ellipse314's user avatar