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Questions tagged [oscillations]

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3
votes
1answer
85 views

How do multigrid approaches deal with Gibbs phenomenon?

I know (from https://scicomp.stackexchange.com/a/31339/20545, among others) that I need a certain mesh density in FEM, else I might get non-physical oscillations in my solution. How do multigrid ...
11
votes
3answers
280 views

Numerical evaluation of highly oscillatory integral

In this advanced course on applications of complex function theory at one point in an exercise the highly oscillatory integral $$I(\lambda)=\int_{-\infty}^{\infty} \cos (\lambda \cos x) \frac{\sin x}...
3
votes
2answers
100 views

Damped Harmonic Oscillation. Efficient algorithm to find the parameters resulting in threshold oscillation amplitude

Let's assume, that we have damped harmonic oscillation of a body in the form of a cone, immersed in a liquid. Equilibrium condition of the body is: $$m\overrightarrow{a} = \overrightarrow{F_\text{...
8
votes
1answer
162 views

What are these oscillations?

I have a function $g(x)$ defined numerically that is sort of in between a Gaussian and a Lorentzian. It decays much slower than a Gaussian, but still faster than a simple inverse power. I need to ...
0
votes
1answer
147 views

Unphysical Behaviour Characteristic-Wise WENO5-Z

I am currently working on a scheme that uses finite differences WENO5-Z with 3rd Order Runge-Kutta time integration for solving the Euler equations. The code projects the conserved variables and ...
1
vote
0answers
171 views

Odd-even decoupling at faces of cells

I am currently solving PDEs using the finite volume method. The surface integrals of the equations that I am solving involves computing face gradients. The current algorithm that we use to compute ...
1
vote
1answer
55 views

Methods for integration of oscillatory complex vectors as a function of time

I'm attempting to solve a problem of the form: $$ \mathbf{a}^{(n+1)}(t) = \int_{0}^{t}d\tau e^{i\mathbf{H}\tau} \mathbf{D}(\tau)e^{-i\mathbf{H}\tau}\mathbf{a}^{(n)}(\tau) $$ Where $\mathbf{D}(\tau)$ ...
5
votes
1answer
1k views

What is the origin of the spurious oscillations in the Crank-Nicolson scheme?

I was reading about the Crank-Nicolson method, and it is often said that it can produce "spurious oscillations" or that this method is prone to "ringing", especially for large time step and stiff ...
1
vote
0answers
126 views

Preventing numerical oscillations with Cash-Karp method

I am implementing an ODE solver using the Cash-Karp method on equations with the following form: $$ \frac {d E}{d z} = - \frac {1}{\mu_0c} \frac {d ^2 E}{d z^2} + \frac {i}{\mu_0c}E \tag{1} $$ And ...
4
votes
1answer
85 views

Post-processing the noisy results of numerical simulation

I have the following curve, which is calculated on a large number of points and shows smooth behaviour when viewed from distance. However, the derivative (shown below) exhibits artificial ...
3
votes
2answers
143 views

Numerical methods for the $u_t + \frac{(u_x)^2}{2} = 0$ equation

I'm looking for some methods that could be directly applied to the PDE $$ \frac{\partial u}{\partial t} + \frac{(u_x)^2}{2} = 0\tag{*} $$ without converting it by $v = u_x$ to the Hopf equation $$ \...
1
vote
0answers
58 views

“Damping factor” for a set of non-linear ODEs

I have a set of four non-linear ODEs representing a negative feedback. I have done parameter variation by random sampling to study the sensitivity of steady state and other dynamic properties to ...
1
vote
1answer
99 views

alternatives to moving mesh technique

If one has to simulate oscillating plate/solid wall ( sinusoidal function of time) in a domain (a simple piston movement in 'y' direction), the obvious way would be scenario 1. For brevity, assume ...
1
vote
3answers
179 views

Fast way to compute integral of type $\int dx f(x) \cos(n \pi x)$ in SciPy

I have an integral of the form $$ I(n) = \int_0^1 dx f(x) \cos(n \pi x) , $$ where $n$ is an integer. In other words, I calculate the cosine Fourier coefficients of function $f$, which is real and ...
3
votes
0answers
93 views

Numerical Quadrature of Oscillating Integral With Non-oscillating part

As you will know there are different numerical integrals (I believe Levin's method is the most popular one) for the numerical quadrature of oscillating integrands which may roughly speaking be written ...
3
votes
1answer
193 views

How to detect specific behavior in time series?

I was not quite sure what the right SE for this was, so I posted this also here on DSP. Please tell me which one to remove :) Problem statement I have a few hundred unrelated time series, say $P_i(t)...
3
votes
1answer
193 views

boundary oscillations with Robin boundary conditions

When solving Poisson's equation on the unit square $\Omega$ with homogeneous Dirichlet boundary conditions for $x=0$ and Robin-type conditions at the rest of the boundary, $$ \begin{cases} -\Delta u = ...