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Questions tagged [numerical-methods]

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Questions on numerical methods; methods for approximately solving various problems that often do not admit exact solutions. Such problems can be in various fields. Numerical methods provide a way to solve problems quickly and easily compared to analytic solutions.

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Recurrence formula for $\pi$ with convergence order $2m+1$: $$ x_{n+1} = x_n + \sum_{k=1}^{m} \left[ (-1)^{m+k} \cdot \frac{1}{k} \prod_{\substack{j=1 \\ j \ne k}}^{m} \frac{j^{2}}{k^{2} - j^{2}} \...
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I'm trying to find a problem about right triangles with a minimalist statement that isn't too obvious. Here's what I've come up with : ABC is an A–right triangle, H is the orthogonal projection of A ...
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I am given f(x)=cosh(x) and asked to estimate f’(0.6) using Richardson Extrapolation to the highest possible accuracy. I computed the centered difference using h1=0.2 and h2=h1/2=0.1 I got D(0.1)=0....
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I have a certain dataset which contains $x-y$ components of a vector quantity $\vec{F}$. The $x-y$ points are such that they essentially discretize a curve which encloses the origin. I want to compute ...
ishan_ae's user avatar
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The algorithm is quite simple. Let's start with some definitions. Take an integer $k$ of length $N$ we can denote its digits from left to right as $k=k_0k_1... k_{N-1}$. Now let $k_{rev}$ be the ...
AgentM's user avatar
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For reasons not directly relevant to the question, I am constructing a function basis in $\mathbb{R}^3$ by taking the tensor product of the fourier basis (up to discretization). I must now come up ...
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We have three types of basic numerical differentation: Forward, Backward and Central defined as such: Forward difference (uniform grid) $\frac{df}{dt}\Big|_{t = t_i} \approx \frac{f_{i+1} - f_i}{\...
Leif's user avatar
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I want to pinpoint the times where an output waveform of an electronic circuit has a specific value. This is a root-finding problem but to my knowledge root finders don't guarantee to find all roots ...
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1 vote
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I have several sets of experimental data representing borehole diametrical closure versus distance along a borehole. Each dataset shows a general smooth trend (for example, a small increase followed ...
Saeed's user avatar
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I am trying to get an overview of "all" (usable) numerical conformal mapping methods, and here is what I found/ read up on so far. Anyone who is an expert in the field who wants to correct/ ...
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Consider the equation: $$ \partial_tu=D\partial_{xx}^2u $$ with reflecting boundary condition at $x=0$ and with $u(x,0)=\delta(x)$ as an initial distribution. First question: How should I understand a ...
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Let's suppose that I wanted to compute $\left\|f\right\|_{\infty}=\sup_{t \in \mathcal{T}} \left|f(t)\right|$ for a $f$ that may not be easy to optimize. This is the infinity norm of a function, and ...
cgmil's user avatar
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I’m computing PDE residuals for the The Well datasets (for example turbulent_radiative_layer_2D and shear_flow) using finite-difference methods, but the results are much larger than I expected. ...
Kain's user avatar
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1 answer
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I'm trying to compare my numerical vs exact solution to the anti-derivative of the piecewise function $$u(x)=\begin{cases}1,&x<\frac{\pi}{2}\\2,&\frac{\pi}{2}\leq x<\frac{3\pi}{2}\\1,&...
OzymandiusBlorg's user avatar
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I’m sorry if this has already been answered; I couldn’t find a clear answer (maybe there is an indirect one and I failed to make the connection). In the context of numerical analysis / finite elements ...
alep17's user avatar
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