While reproducing a research paper, I came across the following equation,
∂f/∂t−(H(f)(∂f/∂x)=0
where [H(f)] is hilbert transform of 'f.'
and f=f(x,t) and initial condition is f(x,0)=cos(x) and also has periodic boundary conditions given by
F{H{f(x′,t)}}=i⋅sgn(k)F{f(x,t)},
where F(f(x,t) is...
the problems/challenges that you have to face daily are mostly related to code issues with the physics itself?
Is there room to improve our knowledge of fundamental physics while working on it?
Do you enjoy doing it? why?
I'm asking this because I'm considering working on numerical relativity...
Hi,
I working on code that does image tracking with missing pixels, but I noticed that higher ordered spline interpolation is unstable. Found through trial and error that the best result is degree 3, picture related. I always thought that spline interpolation does not display behaviours shown...
Hello, I am working with numerical relativity and spectral methods. Recently I finished a general elliptic PDE solver using spectral methods, so now I want to do Physics with it. I am interested in solving the lapse equation, which fits into this category of PDEs
$$ \nabla^2 \alpha = \alpha...
Homework Statement
In this problem you will do numerical computer calculations. A skydiver of mass 75.0 kg jumps out of a plane at an altitude of 30.0 km above the surface of the Earth. His parachute fails to open. Assume there is no horizontal motion and the initial velocity is zero. We...
Hi, I'm struggling to understand how the generating polynomials work and are implemented in the difference equation for a general ODE y' = f(t,y)
Difference Equation
Generating polynomials
"Coefficients are normalized either by a_k = 1 or sigma(1) = 1
Hi everyone,
I am trying to find electron wavefunction of a system I am working in. Numerical method I choose is the Variational method (VM). This method is convenient to find the ground state of the system. More details are available here.
Problem I have can be explained on a very simple...
Hello everyone! I am currently playing with an old analog computer, which could solve time-dependent ODE/PDEs pretty fast, without time-stepping. But the problem with analog computer's solutions is that they are not very accurate. I am very curious that is there any numerical method/solver which...
Suppose I have already found the surface normal vectors to a set of points (x,y), how do I compute the surface height z(x,y)?
Basically what I have are the normal vectors at each point (x,y) on a square grid. Then I calculate the vectors u = (x+1,y,z(x+1,y)) - (x,y,z(x,y)) and v =...
Hi,
I am working on TDR (Time Domain Reflectometry). I send a 7GHz bandwidth fast rising edge (14ns) square wave into a coax. I get a return Signal. I have an ADC with 10Msamples/sec. I am using MPLAB IDE for coding the microcontroller.
Now I would like to increase the Points on the...