Questions tagged [integration]
For questions related to integration on computers. This can include numerical approximations of integrals (e.g. Monte Carlo, quadrature, FEM, RK4) and algorithms/software to obtain analytical derivatives (Risch algorithm, SymPy).
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Projecting the initial state on a Discontinuous Galerkin basis
Context
I want to solve a 1D Burgers equation with a discontinuous Galerkin approach on the space-time domain $(x,t)\in [0,1]^2$. I want to project the function $u(x) = e^{-\frac{(x-0.5)^2}{0.02}}$ ...
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Quantifying the inefficiency of Gauss–Hermite quadrature
I am trying to understand the following part of the paper https://doi.org/10.1137/20M1389522 where the author argues about the inefficiency of Gauss-Hermite quadrature.
I think I get the gist of the ...
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Understanding proof of the error bound for Simpson's quadrature rule
I have found the following proof of the error bound for Simpson's quadrature rule:
Using Newton's interpolation method, we derive a cubic polynomial $p_3(x)$ that interpolates $f(x)$ at the points $a, ...
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solve_ivp method=ODE23 time step not decreasing in order
My time step with the function scipy.integrate.solve_ivp is not decreasing in t_span fluctuating (reaching values below or ...
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Implementation of Monte-Carlo Integration
After reading the Wikipedia page for Monte-Carlo integration, I have understood the basic idea but I am having trouble implementing it for a general case.
The integration that I am trying to do is
$$
\...
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Calculating Debye functions to high accuracy (hundreds of bits), is it possible to be faster than generic quadrature?
The Debye functions are defined like so: ${D_n\left(x\right)} = {\frac{n}{x^n} \cdot {\int_0^x{\frac{t^n}{e^t - 1}dt}}}$.
I'm trying to evaluate the functions for $n$ from one to four and for $\left\...
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How to improve and stabilize this code simulating a damped mass-spring oscillator? Runge-Kutta?
I wrote the following function which is simulating a damped mass-spring oscillator. It is being driven by the audio sample input at 44.1 kHz sampling to create the same effect as a resonant bandpass ...
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How to minimize a numerical integration in python?
I need some help to minimize a numerical integration. It's about a classical problem in physics (hydrogen atom). It can be solved analytically but I need to solve it numerically in Python.
We have an ...
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2
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When can I use finite differences for differentiation?
Finite differences are usually used to integrate ODE's and PDE's. However, sometimes they can be used for differentiation which I illustrated simply by using the Matlab code below to differentiate the ...
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How to use a custom OdeSolver in Scipy's solve_ivp
In Scipy's solve_ivp documentation, we see the method argument can be either a string or a user-defined ...
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Optimal quadrature rule for heavy tail measure
I'm looking for a well-thought quadrature rule for this measure
$d\mu(t)=\frac{dt}{t^s}$ for $s\in(0,1)$, the underlying motivation is to compute this integral
$$
\lambda^{s-1}=\frac{1}{\Gamma(1-s)}\...
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Am I doing leapfrog integration correctly?
I wrote this minimal example to examine the Leapfrog integration algorithm.
However, I am not sure it is the correct algorithm, and the listing is giving the correct output.
Is this the Leapfrog ...
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Understanding leapfrog integration algorithm
The leapfrog.cpp is an implementation of leapfrog integration algorithm where f() function is being integrated:
leapfrog.cpp
<...
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Solving system of ODEs, where time derivative approaches infinity due top initial condition
I am trying to solve a problem in python using scipy's solve_ivp. The system of ODEs I am trying to solve is for coupled where I am solving for two time-dependent ...
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2D integrals in Python with specified points of interest
Note: This is my first question on stackexchange; please tell me if I'm doing something incorrectly.
I am trying to calculate a series of a 2D integrals in Python with an integrand that has several ...
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