Algorithms that integrate functions over one or more dimensions using approximation techniques, instead of exact, closed-form solutions using symbolic algebra and calculus. Includes concepts like adaptive quadrature, Monte-Carlo methods, finite element analysis, Markov chains.
I would like to calculate the area under a curve to do integration without defining a function such as in integrate().
My data looks as this:
Date Strike Volatility
2003-01-01 20 0.2
2003-01-01 30 0.3
2003-01-01 …
Program Purpose: Integration. I am implementing an adaptive quadrature (aka numerical integration) algorithm for high dimensions (up to 100). The idea is to randomly break the volume up into smaller sections by evaluating points using a sampling…
I am trying to plot a Fourier integral, but I get error while integrating
X <- seq(-10, 10, by = 0.05)
f_fourier <- function(X) {
Y <- sapply(X, function(x) {
integrand <- function(l) {
y <- (2 / pi) * cos(l * x) / (l^2 + 1)
…
I'm wondering how to code that takes double integrals in R. I already referred two similar questions.
calculating double integrals in R quickly
double integration in R with additional argument
But I'm still confused how I can get my question from…
Okay I know this has been asked before with a limited example for scaling [-1, 1] intervals [a, b] Different intervals for Gauss-Legendre quadrature in numpy BUT no one has posted how to generalize this for [-a, Infinity] (as is done below, but not…
I'm trying to develop a physics simulation and I want to implement a fourth-order symplectic integration method. The problem is that I must be getting the math wrong, since my simulation is not working at all when using the symplectic integrator (as…
I was wondering if anyone knew of a numpy/scipy based python package to numerically integrate a complicated numerical function over a tessellated domain (in my specific case, a 2D domain bounded by a voronoi cell)? In the past I used a couple of…
I am trying to integrate over a constant function in MATLAB 2017a, but I am stuck. First of all when I integrate using the following script, I get the right output. So the script works for a x0 which depends on t.
function E=sol(n,k)
x0 = @(t) …
I have a DataFrame of force-displacement data. The displacement array has been set to the DataFrame index, and the columns are my various force curves for different tests.
How do I calculate the work done (which is "the area under the curve")?
I…
I would appreciate if someone can help with the following issue.
I have the following ODE:
dr/dt = 4*exp(0.8*t) - 0.5*r ,r(0)=2, t[0,1] (1)
I have solved (1) in two different ways.
By means of the Runge-Kutta method (4th order) and by means…
I want to numerically integrate the following:
where
and a, b and β are constants which for simplicity, can all be set to 1.
Neither Matlab using dblquad, nor Mathematica using NIntegrate can deal with the singularity created by the denominator.…
I have written a function to compute the Laplace transform of a function using scipy.integrate.quad. It is not a very sophisticated function and currently performs poorly on the probability density function of an Erlang distribution.
I have included…
How can we use the NumPy package numpy.polynomial.legendre.leggauss over intervals other than [-1, 1]?
The following example compares scipy.integrate.quad to the Gauss-Legendre method over the interval [-1, 1].
import numpy as np
from scipy import…
There is a commonly used verlet-integration formula on the web by Johnathan Dummer, called Time-Corrected Verlet. However I've read several forum posts, that people get weird or unexpected results with it in certain conditions.
Formula by Johnathan…
