All Questions
9 questions
1
vote
1
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15k
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Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression
Hello all,
I've recently been introduced to Python and Numpy, and am still a beginner in applying it for numerical methods. I've been performing simple 1D diffusion computations. I suppose my ...
4
votes
4
answers
944
views
Role of weight function in Galerkin methods
I have difficulties in understanding the role of the weight function $w(x)$ that occurs in the solution of PDEs via the Galerkin approach. Consider a linear differential equation of the form
$$
\...
- 3,237
7
votes
2
answers
455
views
Spectral Methods in time
I was reading up on Spectral Methods for PDEs. In all the descriptions I read, while the position component is approximated via a Fourier series or other methods, the time component is still ...
- 73
4
votes
2
answers
613
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Interpolation with the roots of orthogonal polynomials & Spectral expansion
I'm a bit confused about the relationships between these two approximation methods mentioned in the title.
Does this kind of interpolation also belongs to the field of spectral methods?
Are the ...
- 699
4
votes
1
answer
3k
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How do I form the Chebyshev differentiation matrix in MATLAB?
I have some code that does exactly this, but I do not like to use things I do not understand. Here is the code
...
user21030
3
votes
3
answers
1k
views
Solving Stokes flow with walls using Oseen tensor
Introduction
I've developed a code to solve for generalised, incompressible 2D Stokes flow
$\eta \nabla^2 \mathbf{v} - \nabla p + \mathbf{S} = 0$
$\nabla . \mathbf{v} = 0$
where $\mathbf{S}$ can ...
- 265
3
votes
2
answers
2k
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Solving numerically the 1D Kuramoto-Sivashinsky Equation using spectral methods
Lately, I've been trying to solve numerically the 1D Kuramoto-Sivashinsky Equation using spectral methods.
Let $\nu$ be the viscosity and $[0,L]$ the domain. The 1D equation is,
$$
u_t + uu_x + u_{xx} ...
- 173
2
votes
1
answer
411
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Where am I making a mistake in solving the heat equation using the spectral method (Chebyshev's differentiation matrix)?
I would like to numerically solve the following heat equation problem:
$$ u_t = \Bigg(2{a \over l}\Bigg)^2 u_{xx} \tag 1$$
$$ x \in [ -1, 1 ] \tag 2$$
$$ u(x, 0) = 0 \tag 3$$
$$ u(1, t) = A \sin \Bigg(...
1
vote
1
answer
2k
views
How to solve heat equation in spherical coordinates with finite differences?
I have a problem dealing with heat transfer which is spherically symmetrical. I was thinking it should be possible to solve this as a 1d problem in spherical coordinates using the radius only.
...
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