# Questions tagged [numerical-calculus]

This tag is for various question on numerical calculus / numerical analysis which concerned with all aspects of the numerical solution of a problem, from the theoretical development and understanding of numerical methods to their practical implementation as reliable and efficient computer programs.

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### numerically compute eigenfunctions of $a(u,v)=\langle f(\nabla u)\nabla u,\nabla v\rangle_{L^2}$

Let $D:=(0,1)^2$ and consider the nonnegative form $$a(u,v):=\langle f(\nabla u)\nabla u,\nabla v\rangle_{L^2(D;\:\mathbb R^2)}$$ for $u,v\in L^2(D)$ where $f:\mathbb R^2\to(0,\infty)$ is a smooth ...
24 views

### diverging determinate of numpy eigenvalues

I am trying to solve the equation $u''=\lambda u$ via discretized matrix scheme. Therefore, as a first step, I need to compute the eigenvalues $\lambda$ using the numpy.linalg.eigvals function. If I ...
24 views

### Help with theory part to be able to implement Advection diffusion into MATLAB code.

I am solving the 1-D advection-diffusion equation, but I am stuck on how to implement the formula into my code. I understand how to the the next time step when the advection term and diffusion term ...
1 vote
23 views

### Quasi-Monte Carlo Integration of Probability Density With Light Tails

I want to integrate $$f(x) = (2\pi)^{-\frac{p}2}\operatorname{det}(\Sigma)^{-\frac 12}\exp\left(-\frac 12 (x-\mu)'\Sigma^{-1}(x-\mu)\right)$$ over the $p$-dimensional hypercube $[a,b]^p$. Since $p$ ...
43 views

### Point in use of Taylor Series to approximate functions in an age with computers?

I hope this doesn't sound too vague or like I'm dismissing the use of Taylor Series entirely, I'm just curious about any proper real-world applications. Many times Taylor Series are shown-off as a ...
46 views

### Numerically compute an oscillating series

I would like to compute in a numerically stable way an oscillating series. Imagine I have a signal $C(n)$, $n\in\mathbb{N}$ which decays exponentially with $n$ e.g. $C(n) = e^{-2n}$. Also, imagine I ...
30 views

### Approximation of product or product of approximations?

I came to an interesting question that I cannot easily answer. There is a uniform grid $x = {x_1, \dots, x_{i-1}, x_{i}, \dots, x_n}$. Values of two functions that are not known analytically are given ...