I'm writing code to numerically solve a single variable equation, currently with Newton Raphson's method. Right now, I'm just using an initial guess of 1, and reporting a failure if it doesn't converge. While it usually works, it does of course fails for many functions with asymptotes or other...
The time rate of change of neutron abundance ##X_n## is given by
$$\frac{dX_n}{dt} = \lambda - (\lambda + \hat\lambda)X_n$$
where ##\lambda## is neutron production rate per proton and ##\hat\lambda## is neutron destruction rate per neutron.
Given the values of ##\lambda## and ##\hat\lambda## at...
Summary: How to calculate the equilibrium angle of a bar that is lifted on its two ends with ropes attached to fixed lifting points?
Hello and good day all,
First of all I would like to apologize in advance for my english, I am not a native speaker so some grammar errors may be left.
My...
◎ As Structural Design Engineer,
Highly-motivated individual with a demonstrated history in Finite Element Analysis to solve complex structural
engineering problems, applying numerical methods approach and view solution results (Post- Processing) to
optimize the design of a Ship to Shore (STS)...
Summary: different methods give different results. They are not consistent.
Summary: different methods give different results. They are not consistent.
I use two different methods to detect whether a matrix is singular. The result of calculating the determinant of a 9-order square matrix is...
Hello and thanks in advance for your help.
For about a week now, I've been trying to write what should be a simple python program. The idea is first to write a program for a simple harmonic pendulum, then adapt it to a spring pendulum. However, in order to do this, I have to write the simple...
Hi,
I hope I am in the right section of the forum. I was trying to understand the following algorithm:
https://benchmarksgame-team.pages.debian.net/benchmarksgame/program/nbody-python3-1.html
and particulary this part:
def advance(dt, n, bodies=SYSTEM, pairs=PAIRS):
for i in range(n)...
For Initial Value problems I want to implement an ODE solver for implicit Euler method with adaptive time step and use step doubling to estimate error. I have found some reading stuff about adaptive time step and error estimation using step doubling but those are mostly related to RK methods. I...
I am doing DMRG (in traditional formalism, not MPS) for Hubbard model
H = -t ∑i ∑σci,σ ci+1,σ + U∑ini,σni,σ-
In every iteration we add two sites to the system, but how do we set that how many particles are allowed in the system?
Hello! I am trying to write a program that solves the Schrodinger Equation for a particle in an infinite square well. I did a lot of research regarding the methods that could be used to accomplish this. I am writing this program in Matlab. The method I am using is called the Shooting Method. In...
Hi all, I'm trying to compute the solutions to a general case for a Schroedinger equation with a radial potential but I'm stuck on a rather small detail that I'm not sure about. It's well known that I can perform the change of variables to spherical coordinates and express the radial part of the...
I am using arpack (the dsdrv1 driver) to iteratively solve the eigenvalue problem
Ax = λx
I am interested in the first m eigenvectors, and I have very good initial approximations for these vectors, so I would like to use my m starting vectors as an initial guess. However...
I have a Hamiltonian represented by a penta-diagonal matrix
The first bands are directly adjascent to the diagonals. The other two bands are N places above and below the diagonal.
Can anyone recommend an efficient algorithm or routine for finding the eigenvalues and eigenvectors?
I attempt to solve the brachistochrone problem numerically. I am using a direct method which considers the curve ##y(x)## as a Lagrange polynomial evaluated at fixed nodes ##x_i##, and the time functional as a multivariate function of the ##y_i##. The classical statement of the problem requires...
Hi,I'd like to build a simulation (realtime) of space ships near a black hole (neutral, still or rotating possibly). Key features would be:
1) the ships are test particles that do not affect the metric
a) possibly test rigid-bodies with GR consistent rotational DOF.
2) the ships can fire...
Hi, I have been trying to use imaginary time propagation to get the ground state and excited states eigen function but the results I got is different from the analytical solution. I know that to get excited states, I should propagate 2 or more orthogonal functions depending on the number of...
From the Theory of Open Quantum Systems; the Euler scheme is given by:
##\psi_{k+1} = \psi_{k} + D_1(\psi_k)\Delta t + D_2(\psi_k) \Delta W_k##
and is a scheme of order 1. What does the order of convergence mean? From my understanding higher order schemes require fewer interations to give a...
All matrices A\in\mathbb{C}^{n\times n} have at least one eigenvector z\in\mathbb{C}^n. I'm interested to know what kind of algorithms there are for the purpose of finding an eigenvector.
I noticed that
\frac{|z^{\dagger} A z|}{\|Az\|} = 1\quad\quad\quad\quad (1)
holds only when z is an...