# Tag Info

### Shallow-water equations on a rotating sphere by using the NDSolve method with a purpose of earthquake-generated tsunami simulation

Its difficult or hopeless to NDSolve waves on a sphere with boundaries because the governing Laplacian has discrete spectrum. Eigenfunctions of the Laplacian with non-integer eigenvalues belong to ...
• 3,965

### How to solve the partial differential equations?

Check the Neumann-conditions! Try ...

### How to solve the partial differential equations?

The inhomogenuous equation $$\Delta_{x,y}\left(-e^x \ \sin (\pi y) +g(x,y)\right) == \ e^x \ \sin (\pi y)$$ results in the homogenous equation. $$\Delta_{x,y} g(x,y)==0$$ Reformulate the other ...
• 3,965

### How to increase the mesh size in NDsolve

You can do that though a Method option but the exact option dependents on whether the DE is stationary or time dependent: ...
• 40.1k

### Boundary conditions issue with Laplace equation

In Version 14.0 this works: ...
• 40.1k
Accepted

### Boundary conditions issue with Laplace equation

We can use OpenCascadeLink to generate mesh for this problem as follows (note, we rescale l, r, rs because the solution does not ...
• 46.4k
Accepted

### Numerically solved PDE of Ornsteinâ€“Uhlenbeck process on 2-Simplex violates conservation of probability

The initial condition was inconsistent and needed to exclude the boundary: ...
1 vote

### Boundary conditions issue with Laplace equation

It works if you remove one of the two balls. For example : : ...
• 18.7k

### Numerically solved PDE of Ornsteinâ€“Uhlenbeck process on 2-Simplex violates conservation of probability

Roughly your equation is $$\ \partial_t P =-\left(\frac{3}{2}\ - \ y \right) \ \partial_y \ P \ -\left(\frac{5}{2}-x \right) \partial_x \ P +\frac{1}{2}\Delta \ P \ + \frac{3}{2} \ P$$ by the fact ...
• 3,965
Accepted

### Numerical solution with both Neuman and Drichlet BC at one point

Using my code from here we have ...
• 46.4k
Accepted

### How is the result of this integral obtained by the function Integrate?

I'm not sure if this is an intended behavior or a bug in Mathematica's end, but it does make sense to get different results. Below, I show how to get both results as desired. EDIT: Some people ...
• 2,194
1 vote

...
• 81.9k
1 vote
Accepted

Semi-numeric ...
• 14.7k

### Unexpected problem while integrating the Weierstrass $\wp$ function

For unknown reasons, WeierstrassInvariants and WeierstrassP with accurate arguments due not evaluate to numbers with precision of 100. However, if you convert the integrand to precision of 100 it will ...
• 53.7k

### Approximate value for the area between the curve

Using IntegralApproximationPlot by Dennis M Schneider ...
• 81.9k
1 vote

### Partial Derivative after Numerical Integration of a Complicated Expression with Singularity at Zero

Maybe this can get you going, not sure it is all correct, the graph looks a bit different, but maybe with more points and fixing ColorFunction and ...
• 17.2k
1 vote

### Partial Derivative after Numerical Integration of a Complicated Expression with Singularity at Zero

Do you realize that you have about 1.97506*10^10 oscillations per unit change in k for smallish ...
• 239k
Accepted

### How to NDSolve a PDE that contains the integral of the solution?

We can solve this problem using method of lines as follows ...
• 46.4k
1 vote

Workaround: ...
• 14.7k

### How is the result of this integral obtained by the function Integrate?

It is a bug in Integrate. The numerical result seems to be the correct one. You can use Rubi integrator for workaround meanwhile. ...
• 147k

### I have a problem with this code because it is time invertible symmetric but it is not working

Although the question is not entirely clear to me, I presume that a solution symmetric about x = 0 is desired. To produce such a solution, both the ODE and its ...
• 61.8k

### Integrating over an interval

[H]ow do I integrate v from xmin to x_1, then x_1 to <...
• 239k
The latest packages for PDE use DirchletCondition as a container for the boundary condtions of the unknowns and for Neumann boundary conditions replace the right side $eq==0$ by a source term, that ...