Linked Questions

54 votes
4 answers
8k views

Dynamic Euler–Bernoulli beam equation

I am trying to solve for the vibration of a Euler–Bernoulli beam. The equation is $\frac{\partial ^2u(t,x)}{\partial t^2}+\frac{\partial ^4u(t,x)}{\partial x^4}=0$ For the boundary conditions I ...
Hugh's user avatar
  • 16.5k
31 votes
3 answers
4k views

1D Euler equations (fluid dynamics) with NDSolve

Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve? For example, let us consider the Sod shock tube problem. Introduction to ...
partition_of_unity's user avatar
12 votes
4 answers
1k views

Solving Burger's equation with NDSolve at large time

I want to solve the following Burger's equation $$\partial_tu+\partial_x\left(\frac{u^2}{2}\right)=0,~~x\in[0,2\pi],~t>0\\u(x,0)=\frac{1}{3}+\frac{2}{3}\sin(x)$$ with mathematica. Here's my code: <...
Ho-Oh's user avatar
  • 245
9 votes
2 answers
679 views

Why does NonlinearStateSpaceModel linearise?

The documentation for NonlinearStateSpaceModel says: In NonlinearStateSpaceModel[eqns, ...] the Taylor linearization is with ...
CarbonFlambe's user avatar
  • 1,234
3 votes
2 answers
437 views

how to fix this PDE numerical solution (NDSolve)

I have the following code: ...
user56834's user avatar
  • 545
7 votes
1 answer
561 views

Can NDSolve address spherical gravitational collapse?

As far as I know spherical gravitational collapse -of central importance to theoretical physics- is thought to be out of the scope of Wolfram Mathematica. However there are cases, as in this article,...
user avatar
1 vote
1 answer
229 views

Solving 3 nonlinear, transient, coupled PDEs [closed]

I'm trying to solve the fluid equations, continuity equations for mass, momentum, and energy, for a transient shockwave in 1D planar geometry. A piston is traveling at some velocity $u_p$ where $u_P$ $...
Liam's user avatar
  • 21
4 votes
1 answer
199 views

NDSolve Warning: an insufficient number of boundary conditions. However, all boundary conditions are defined

I am trying to solve the system of equations (momentum conservation, heat, and polymerization equations) in the Couette problem. There are two planes, the bottom is fixed, the top is moving with the ...
Eugene W.'s user avatar
  • 143
0 votes
0 answers
160 views

Problem with definition of boundary problem

My procedure for solving coupled 1 + 1 (spatial + temporal) PDE system: (Note: I have graphs of the correct solution with which I compare my result. See figure below text.) 1) I determine the ...
Vrbic's user avatar
  • 75
0 votes
0 answers
91 views

Need a method to solve a nonlinear PDE with gradients of the same order as the PDE's

I have a system of first order non-linear PDE's, but some of my boundary conditions are also of first order, so mathematica cannot solve it. When I looked online for similar problems , I found some ...
Hidde Rinsema's user avatar