12
votes
Accepted
Solving Burger's equation with NDSolve at large time
Similar problems have been discussed in this site for several times:
Solution of Burgers equation with some initial data
1D Euler equations (fluid dynamics) with NDSolve
Circumvent NDSolve::bdord: ...
- 51.5k
10
votes
Solving Burger's equation with NDSolve at large time
The answer of Nasser is only in parts correct. The analytic/implicit solution
$$
u(x,t) = f(\xi) = f(x-ut), \quad \xi = x - f(\xi) t
$$
is only the physical solution in the interval $0\le t \le t_b$ ...
- 2,240
9
votes
Solving Burger's equation with NDSolve at large time
Following the example set by xzczd's answer: an alternative to an external library would be to implement a simple shock capturing finite volume scheme like the one put forward in New High-Resolution ...
- 2,240
6
votes
Solving a nonlinear integral equation
This integral equation can be transformed into a system of ODEs, after which it can be solved with NDSolve. Begin with the integral equation,
...
- 58.2k
6
votes
Solving Burger's equation with NDSolve at large time
I am not sure if there are options to improve NDSolve. I tried stiffness method, but that did not help.
But since the inviscid Burgers' equation has analytical solution, then you can use that.
Where $...
- 108k
4
votes
Accepted
3
votes
Accepted
Abs applied with explicit map not giving same result as built in threading
I observed similar behavior in a number of vectorized functions around five years ago. Since I figured it out to the extent possible, without knowing the details of the Math Kernel Library and how it ...
- 213k
3
votes
Accepted
Nonlinear Schrödinger Equation With Periodically Varying Function
There is a typo in the paper Self-imaging in multimode graded-index fibers and its impact on the nonlinear phenomena by Govind P. Agrawal. With initial condition $u(0,\tau)=Sech(\tau)$ this problem ...
- 33.7k
2
votes
Is it possible to solve a differential equation with a user-defined variable mesh in NDSolve?
This is hard (if not impossible) to achieve inside NDSolve AFAIK. I sincerely hope I'm wrong. As mentioned in the tutorial The Numerical Method of Lines, ...
2
votes
Numerically solving nonlinear PDE $u_t = G(u,u_y,u_{xy},u_{xx}u_{yy})$ with unbounded initial condition
We can use properties of asymptotic solution $u_*$ and that solution of equation $u_t=(d+2)u-d y u_y+V_i(t,x,y)$ defined well with polynomial initial condition and boundary condition ...
- 33.7k
1
vote
Finding local minimum of a 2D potential
There is a local minimum. Rationalize parameter and first search for minimum curve with respect to chi. This can be achieved by intermediate substitution of exp term.
...
- 15.2k
1
vote
How to import a file with 3 columns of numerical data and visualize it with ListPointPlot3D?
Try using
Import["/PATH/file.txt", "Table"];
This will convert each data point into a 2-D list. From, there you can easily plot any column with ...
- 393
1
vote
Numerically solving nonlinear PDE $u_t = G(u,u_y,u_{xy},u_{xx}u_{yy})$ with unbounded initial condition
As a supplement to @AlexTrounev nice answer NestList might simplify the code of iteration:
...
- 36.4k
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