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Questions tagged [numerical-integration]

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Questions on the use of numerical functions NIntegrate and NDSolve.

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I am trying to solve an iterative matrix ODE of the form $f_k'(x)=T.f_k(x)+B(x)*S.f_{k-1}(x)$, where f is an $n$ dimension column, T and S are $n \times n$ matrices, and $B(x)$ is a function. The ...
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I'm solving an ODE system with multiple events and find the discrete variable not updated as expected because one of the events is not triggered. During narrowing down the problem, I find something ...
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A lofted solid is like a solid cylinder with two different end caps. A natural set of questions given a lofted solid using two shapes would be if we were to be able to rotate an end around the ends ...
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I the following ODE with parameters \begin{align} B_e\: \theta''(s)+2(s-1)\cos\theta(s)=S_e\: f\left(\theta(s)\right), \end{align} with $0\leq s\leq 1$ and \begin{align} \theta(0)=0\:\:\:\text{and}\:\:...
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I have been working on a wiki page about asymptotic Laurent series for derangements, and recently learned that the converse of Watson's lemma often holds, allowing one to represent such series as ...
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I have an integral that I want to integrate over the whole $\mathbb{C}$ plane, say parametrized by $(z,\bar{z})$. The integrand is of the following form $$ \frac{f(z,\bar{z})}{|1-z|^2} - \frac{C}{|1-z|...
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I am hitting a problem with numerical integration. I have a function (a4xinteg in this expression below), the expression is quite long so below you can find a plot of it: I would like to integrate ...
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Suppose we have two interpolating functions with exactly touching domains, in our case {-1, 1} and {1, 2}. How to "glue&...
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I want to find for which t any of these holds: x[t] + y[t] == 0.25, x[t] + y[t] == 0.5, <...
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I'm solving the Regge–Wheeler equation in Schwarzschild spacetime D[u[t, x], {t, 2}] + Vsx[x]*u[t, x] == D[u[t, x], {x, 2}], with the potential ...
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Could someone please explain me why these errors happen and if it's possible to solve them? Here's my code ...
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Is there a way to obtain the error on a numerical integration using NIntegrate ? I have try this answer https://mathematica.stackexchange.com/a/102469/111297, ...
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I would like to reproduce the Poincaré sections presented in this and this papers, which look like The figures are for energy values of E=0.2 (a) and E=0.25 (b) in the Hamiltonian, which reads $$H=\...
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There is a need to increase the number of correct decimal digits from this integral: ...
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I'm trying to solve the equation \begin{align} \epsilon_b\:\theta''(s)-(l-s)\cos\theta(s)=\epsilon_\gamma\sin\theta(s)\cos\theta(s), \end{align} with $0\leq s\leq l$ and \begin{align} \theta(0)=0\:\:\:...
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I want to analytically integrate this integration $$\int_0^{1 - 3/rs}\left(\frac{9 \sqrt{3} \sqrt{\frac{1}{\left(1-\frac{2}{\eta }\right) \eta ^2 \left(\frac{\eta ^2}{1-\frac{2}{\eta }}-27\right)}}}...
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I want to integrate a function like NIntegrate[f[x1] g[x2], {x1, 0, L}, {x2, x1, L}] which is a triangle region. For every x1, ...
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The following code ...
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I am interested in Fomes Fomentarius or "Tinder Polypore" mushroom patterns (original photo, diagrams of Voronoi and Delaunay): At first it seems something simple, like a sunflower seed ...
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I have a function which I want to integrate and then plot. The function is a complicated one and getting an error SystemException["MemoryAllocationFailure"]. Can any one fix this? The code ...
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I'm working on finding the limit of a function that involves nested integration. I've written the code, and it's running an iterative procedure. However, each iteration currently takes about 24 hours ...
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I applied the recommendations from my previous question, the calculation time was reduced. Thank you very much! Now I have a question regarding the calculation of some matrix elements, for example <...
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The code below is used to calculate the matrix elements He. However, the calculation of each element takes a very long time. Question: How can the speed of these ...
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I was hoping to solve a two dimensional integration equation, which is actually a simplified Schrodinger equation in momentum space: $$ (x^2-3)f(x,y)-\int_0^\infty du\int_0^{\pi}dv\frac{u^2\sin{v}f(...
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edited The gaussian quadrature rules are very helpful in solving many numerical problems. Unfortunately Mathematica only provides the one dimensional rules in the package ...
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