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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 ...
Roland F's user avatar
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2 votes

How to solve the partial differential equations?

Check the Neumann-conditions! Try ...
Ulrich Neumann's user avatar
-1 votes

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 ...
Roland F's user avatar
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3 votes

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: ...
user21's user avatar
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2 votes

Boundary conditions issue with Laplace equation

In Version 14.0 this works: ...
user21's user avatar
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4 votes
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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 ...
Alex Trounev's user avatar
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0 votes
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Numerically solved PDE of Ornstein–Uhlenbeck process on 2-Simplex violates conservation of probability

The initial condition was inconsistent and needed to exclude the boundary: ...
CRTmonitor's user avatar
1 vote

Boundary conditions issue with Laplace equation

It works if you remove one of the two balls. For example : : ...
andre314's user avatar
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0 votes

Numerically solved PDE of Ornstein–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 ...
Roland F's user avatar
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3 votes
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Numerical solution with both Neuman and Drichlet BC at one point

Using my code from here we have ...
Alex Trounev's user avatar
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6 votes
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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 ...
SonerAlbayrak's user avatar
1 vote

Numerical approximation of the integral by using data

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eldo's user avatar
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1 vote
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How to numerically integrate the following expression?

Semi-numeric ...
Mariusz Iwaniuk's user avatar
2 votes

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 ...
Daniel Huber's user avatar
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2 votes

Approximate value for the area between the curve

Using IntegralApproximationPlot by Dennis M Schneider ...
eldo's user avatar
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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 ...
Rolf Mertig's user avatar
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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 ...
Michael E2's user avatar
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6 votes
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How to NDSolve a PDE that contains the integral of the solution?

We can solve this problem using method of lines as follows ...
Alex Trounev's user avatar
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1 vote

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

Workaround: ...
Mariusz Iwaniuk's user avatar
2 votes

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. ...
Nasser's user avatar
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0 votes

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 ...
bbgodfrey's user avatar
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0 votes

Integrating over an interval

[H]ow do I integrate v from xmin to x_1, then x_1 to <...
Michael E2's user avatar
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0 votes

Solving partial differential algebraic equation in Mathematica

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 ...
Roland F's user avatar
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2 votes

Numerical approximation of the integral by using data

...
eldo's user avatar
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