Linked Questions

12 votes
3 answers
1k views

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
2k views

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
1k views

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
628 views

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
645 views

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
814 views

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
306 views

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
389 views

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
217 views

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
185 views

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
117 views

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
84 views

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