Linked Questions

58 votes
3 answers

Is manual adjustment of AccuracyGoal and PrecisionGoal useless?

This is a problem confusing me for years. AccuracyGoal and PrecisionGoal are two options that I never truly understand and, to ...
xzczd's user avatar
  • 66.2k
25 votes
3 answers

Is there any possibility to implement a structure like a ProgressIndicator into NDSolve?

It is already formulated in the title. NDSolve takes sometimes a considerable piece of time. It would be very practical to have some information on how long it is still to wait. So, any ideas? To ...
Alexei Boulbitch's user avatar
12 votes
4 answers

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
22 votes
2 answers

NDSolve uses different difference order for different spatial derivative when solving PDE

I found something this tutorial for method of line doesn't tell us. Consider the following toy example: ...
xzczd's user avatar
  • 66.2k
11 votes
3 answers

Laplace's equation in spherical coordinates with Neumann b.c

I am trying to find the temperature field in a semi-infinite solid on whose surface there is an isotherm spherical cap sunken by a length p. For example: ...
umby's user avatar
  • 585
14 votes
2 answers

Extending NDSolve beyond a singularity

The $\tan$ function satisfies the following IVP: $$y'=1+y^2 ,\quad y(0)=0 $$ and has simple poles at the points $x=\pi/2+ \pi n$ for integer $n$. When trying to get $\tan$ via numerical integration,...
user1337's user avatar
  • 1,078
11 votes
1 answer

Boundary sphere partial differential equation

I am trying to solve partial differential equation in spherical coordinates $(\theta,\phi)$,but I don't know how to properly include boundary conditions of $\theta$. For $\phi$ it is periodic, but $\...
WoofDoggy's user avatar
  • 314
13 votes
1 answer

PDEs : automatic method choice : TensorProductGrid or FiniteElement?

A problem that arises when we solve PDEs with NDSolve[] and Method->Automatic is how to know which method has been chosen : <...
andre314's user avatar
  • 18.5k
6 votes
2 answers

NDSolve for Laplace equation on disk is not working

I want to solve the laplace equation on the disk using NDSolve. Particularly I want to solve the problem $$\frac{\partial^2 u }{\partial r^2 } +r^{-1}\frac{\partial u }{\partial r }+r^{-2}\frac{\...
paradox's user avatar
  • 173
8 votes
1 answer

Droplet of water-alcohol mixture spreading due to evaporation-caused surface tension gradient

I am trying to solve a coupled system of PDEs for 2 functions h[t,r] and c[t,r], with initial conditions of ...
James He's user avatar
7 votes
1 answer

Problems with DSolve and NDSolve for Dirichlet problem on an annulus

To solve the Dirichlet problem on an annulus, I do the following in 12.2 on Windows 10 Pro ...
user64494's user avatar
  • 26.4k
1 vote
1 answer

Solving Laplace equation in spherical coordinates

I was trying to solve Laplace's equation for a spherical capacitor, which is not difficult by hand, just to figure out the commands so I can eventually try something more complicated. Then, I ran into ...
ions me's user avatar
  • 881
3 votes
2 answers

Inactive nonlinear ODE system results in NDSolveValue::femcnmd warning

I am currently trying to solve a set of 1D steady state ODEs using NDSolveValue in the form of Inactive[Grad] and ...
Johnson's user avatar
  • 357
4 votes
1 answer

Modified Helmholtz Equation in Spherical Coordinates

Writing out the Modified Helmholtz equation in spherically symmetric co-ordinates Note that $\nabla^2 \psi(r)\;$=$\;\frac{d^{2} \psi}{d r^{2}}+\frac{2}{r} \frac{d \psi}{d r}$=$\frac{1}{r} \frac{d^{2}}{...
arny's user avatar
  • 79