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: ...
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  • 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 $0\le t \le t_b$ ...
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  • 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 ...
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  • 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, ...
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  • 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 $...
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  • 108k
4 votes
Accepted

Inconsistent results between NIntegrate and Integrate

If you look at the result of ...
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  • 16.7k
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 ...
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  • 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 ...
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  • 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 ...
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  • 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. ...
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  • 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 ...
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  • 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: ...
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