All Questions
Tagged with finite-difference numerics
154
questions
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33
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Imposing higher order finite difference schemes for boundary value problems on a finite interval
I have some questions. I'm going to assume everything is in 1d with a Laplacian operator. If I discretize the Laplacian operator using $p = 2a+1$ grid points with periodic boundary conditions, I ...
- 111
1
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0
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96
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Implicit-Explicit Operator Splitting Scheme
I am trying to solve the 2D advection-diffusion equation in cylindrical coordinates:
$$
\frac{\partial c}{\partial t} = D\left(\frac{\partial^2 c}{\partial r^2} + \frac{1}{r}\frac{\partial c}{\partial ...
- 11
0
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53
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Prof A. Stanoyevitch's finite difference based PDE matlab code
Where can one find Prof A. Stanoyevitch's finite difference based PDE matlab code? They have a book on such a topic but can't find the accompanying code.
Is it well received? It's not commonly talked ...
- 317
3
votes
1
answer
277
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How to evaluate the points near/at the boundary when using Richardson extrapolation for improved accuracy of a derivative
If we want to improve the accuracy of our numerical estimation of a derivative, we can use Richardson extrapolation. The method is very beneficial when using a centered difference scheme and the ...
0
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47
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2nd-order backward difference approximation for temporal terms of Euler–Bernoulli beam
I am trying to solve the Euler–Bernoulli beam numerically in structural dynamics analysis:
$$\frac{\partial^2w(x,t)}{\partial t^2}= \frac {q(x,t)}{\mu(x)}-\frac {1}{\mu(x)}\frac {\partial^2}{\partial ...
1
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1
answer
139
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Best finite difference scheme in 2D for the mixed derivative
The are good methods to deduce finite difference schemes for derivatives of functions of one variable. But how to get a good one for the mixed derivative of a function of two variables $u=u(x,y)$, ...
- 113
0
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39
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Convergence of Modified Crank-Nicolson Scheme
I'm dealing with a particular reaction-diffusion equation having the form
$$ c_t = \alpha \nabla^2 c + F(c,x,t). \tag{1}$$
where $F$ is nonlinear. I would like to solve (1) with a finite-difference ...
- 101
0
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109
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Solving a steady-state PDE
I'm working on trying to solve a steady state PDE in python and I am quite new to python and I am slightly confused on the implementation details. I have an example implementation of solving a non-...
- 43
4
votes
1
answer
148
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Burger's equation (PDE) does not work with downwind difference?
I'm working on implementing the discretised Burger's equation. I am quite confused as to why it does not work when using a step-function and downwind difference formula. When using a step-function and ...
- 43
3
votes
1
answer
280
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Finite difference problem
I have a problem to resolve with the Finite Difference method in $[a,b]$:
$$-\frac{d}{dx}(\alpha(x)\frac{du}{dx})= g(x),$$
with $\alpha(x) \in L^{\infty}$ continuous in $]a,c[$ and $]c,b[$ and ...
- 31
1
vote
1
answer
81
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Does anyone know how to add a forcing term at the center of a cicular membrane?
I am here once again searching for wisdom, as some of you might notice I asked a related question a few days ago. And now I am struggling to add a forcing term at the center of the membrane, in order ...
- 31
0
votes
1
answer
211
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Solving the wave equation for a circular membrane in polar cordinates
As you see this mode is not right, unless for what i understand
And the initial conditions were
...
- 31
0
votes
1
answer
129
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Discretization of generalized kinetic term in 2D Poisson partial differential equation
A typical 2D Poisson PDE is given as
$$\nabla^2\varphi(x, y)=f(x, y)$$
where the Laplacian term, $\nabla^2\varphi$, can to some degree be interpreted as the kinetic energy (given proper scaling) (...
- 83
0
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39
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Perfect Conducting (PC) and Perfect Insulating (PI) boundary conditions for magnetic induction in MHD problems in cylindrical coordinates
I understand the computational implementation of the PC and PI bcs in cartesian case. In terms of the magnetic field components for PI, we have $B_x = B_y = B_z = 0$, and for PC, we have $\partial_x ...
- 1
1
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0
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144
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Stability for the 2d diffusion equation
I'm reading this set of notes on numerical stability of the diffusion equation. I can't seem to derive equation (7.17) from the previous equation. I've tried using $\sin^2(\theta)=\frac{1-\cos(2\theta)...
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