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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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Is there any way of regularizing the following integral and showing equality? $$\int \int \int_{\mathbb{R}^3} \exp \left (- i (k_1+k_2)(k_2+k_3)(k_3+k_1) \right ) \, dk_1 dk_2 dk_3 = \frac{2 \pi \ln ...
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Equations of the form $$y = \sin \left(\frac{y^s}{t} - k \right)$$ are surprisingly well approximated as $$y = - \sin k$$ for a large range of $s$ $t$ and $k$ values: Why? I understand why this is so ...
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I am given f(x)=cosh(x) and asked to estimate f’(0.6) using Richardson Extrapolation to the highest possible accuracy. I computed the centered difference using h1=0.2 and h2=h1/2=0.1 I got D(0.1)=0....
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Recurrence formula for $\pi$ with convergence order $2m+1$: $$ 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 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 ...
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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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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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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 ...
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I want to implement a numerical method for conformal mapping of a mesh on the disk to some simply connected bounded Jordan region whose boundary is parametrized by a Fourier series. I was looking at ...
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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}{\...
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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 ...
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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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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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I am trying to proof this by induction Proposition (Boundary values under clamped knots): Let $\{t_i\}_{i=1}^{m=n+k}$ be a clamped knot sequence of order $k$ on the interval $[a,b]$, that is, $$ t_1 = ...
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