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# Questions tagged [oscillations]

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I am trying to simulate the following 1-dimensional wave equation with trivial initial conditions and a inhomogeneous Dirac delta function: $u_{tt} - c^2 u_{xx} = \delta(x - x')\delta(t - t'), \ u(0, ... • 121 5 votes 1 answer 129 views ### Slope limiting with implicit time integration I am solving the advection problem with high order numerical methods, using the method of lines. The boundary conditions and initial condition are selected in a way where I know that the exact ... • 121 2 votes 2 answers 72 views ### How to improve and stabilize this code simulating a damped mass-spring oscillator? Runge-Kutta? I wrote the following function which is simulating a damped mass-spring oscillator. It is being driven by the audio sample input at 44.1 kHz sampling to create the same effect as a resonant bandpass ... • 123 2 votes 1 answer 145 views ### Can this finite difference dispersion be eliminated somehow? I am trying to solve the wave equation $${\partial ^2u(t,x) \over \partial x^2} = {\partial ^2u(t,x) \over \partial t^2} \tag1$$ with the following boundary and initial conditions: $${\partial u \... 0 votes 1 answer 101 views ### Averaging oscillatory data I have an oscillatory data generated vs time as shown below. Essentially, I want this data to be averaged and free of any oscillations. I am not satisfied with the results from a simple moving average ... 0 votes 0 answers 190 views ### Solving differential equations with fast oscillations using odeint I have wrote this code to solve an equation , I know the behavior of this function has very rapid oscillations, when I RUN it gives bogus values for some "m[x]" and some "t"'s, ... • 11 1 vote 1 answer 45 views ### An explanation of 2delta waves on non-staggered grids While looking into the difference between staggered and collocated grids, I came across an effect called 2\Delta x-oscillations, which happen on non-staggered grids, but not on staggered grids. This ... 1 vote 0 answers 61 views ### Good non oscilliatory derivatives for an exsisting grid I'm calculating the entropy production of a shockwave by utilizing the equations: \sigma = J'_q\frac{\partial}{\partial x}\left(\frac{1}{T}\right) +\frac{1}{T}\frac{4\eta}{3}\left(\... • 55 0 votes 1 answer 165 views ### Is it possible to predict solution oscillation before solving the system by looking at coefficient matrix? Question When it is about solving a system of equations, is it possible to predict that whether high-frequency noise (e.g. checker-boarding) is likely to appear in the converged solution by looking at ... • 235 2 votes 1 answer 390 views ### Calculating the Strange Attractor of the Duffing Oscillator in C++ I am simultaneously trying to learn computational physics methods, chaos, and C++. I think this is the right site for the question, and I apologise if not. I started working through Thijssen's ... • 337 1 vote 0 answers 76 views ### Computation of a functional for large values Consider the following function :$$f(x) = \sin^2(\frac{π\Gamma(x)}{2x})$$Now consider the following functional :$$I(x)=\int_0^\infty \frac{f(x + iy) − f(x − iy)}{e^{2πy}-1} dy$$I need values for ... • 119 0 votes 0 answers 130 views ### Scipy.integrate.odeint is returning curves with almost the same frequency for different damping ratios, shouldn't they be different? I am trying to solve the ODE for a harmonic oscillator using Scipy's odeint solver for different dampening factors. I'm using the following code, based off of this example: ... • 101 0 votes 0 answers 2k views ### Solving nonlinear pendulum using Runge-Kutta 4 for smaller steps I am trying to solve nonlinear pendulum using 4th order Runge-Kutta method for limits between a=0.0 to b=110 seconds and simulated the results to observe the pendulum movement. But when I increase the ... • 276 3 votes 1 answer 109 views ### How do multigrid approaches deal with Gibbs phenomenon? I know (from https://scicomp.stackexchange.com/a/31339/20545, among others) that I need a certain mesh density in FEM, else I might get non-physical oscillations in my solution. How do multigrid ... • 553 11 votes 3 answers 940 views ### Numerical evaluation of highly oscillatory integral In this advanced course on applications of complex function theory at one point in an exercise the highly oscillatory integral$$I(\lambda)=\int_{-\infty}^{\infty} \cos (\lambda \cos x) \frac{\sin x}... • 593 3 votes 2 answers 228 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: $$m\overrightarrow{a} = \overrightarrow{F_\text{... 8 votes 1 answer 213 views ### What are these oscillations? I have a function g(x) defined numerically that is sort of in between a Gaussian and a Lorentzian. It decays much slower than a Gaussian, but still faster than a simple inverse power. I need to ... 0 votes 1 answer 227 views ### Unphysical Behaviour Characteristic-Wise WENO5-Z I am currently working on a scheme that uses finite differences WENO5-Z with 3rd Order Runge-Kutta time integration for solving the Euler equations. The code projects the conserved variables and ... • 31 1 vote 0 answers 348 views ### Odd-even decoupling at faces of cells I am currently solving PDEs using the finite volume method. The surface integrals of the equations that I am solving involves computing face gradients. The current algorithm that we use to compute ... • 251 1 vote 1 answer 60 views ### Methods for integration of oscillatory complex vectors as a function of time I'm attempting to solve a problem of the form:$$ \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) $$Where \mathbf{D}(\tau) ... • 1,155 7 votes 1 answer 3k views ### What is the origin of the spurious oscillations in the Crank-Nicolson scheme? I was reading about the Crank-Nicolson method, and it is often said that it can produce "spurious oscillations" or that this method is prone to "ringing", especially for large time step and stiff ... • 71 4 votes 1 answer 100 views ### Post-processing the noisy results of numerical simulation I have the following curve, which is calculated on a large number of points and shows smooth behaviour when viewed from distance. However, the derivative (shown below) exhibits artificial ... • 430 3 votes 2 answers 188 views ### Numerical methods for the u_t + \frac{(u_x)^2}{2} = 0 equation I'm looking for some methods that could be directly applied to the PDE$$ \frac{\partial u}{\partial t} + \frac{(u_x)^2}{2} = 0\tag{*} $$without converting it by v = u_x to the Hopf equation$$ \... • 165 1 vote 0 answers 79 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 ... • 143 1 vote 1 answer 118 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 ... • 21 1 vote 3 answers 336 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 ... • 207 3 votes 0 answers 99 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 ... • 1,119 3 votes 1 answer 221 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)...
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 = ...