# Questions tagged [numerical-methods]

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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### fractional heat equation and spectral method

I want to apply a spectral method for the weak formulation of the equation $(-\Delta)^su=f$ $s>0$ with zero Dirichlet boundary conditions, where $(-\Delta)^s$ shall be the fractional laplacian on ...
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### Numerical method for second order O

Here is a question I got to thinking about while reading speculation about the world being discrete. Suppose I want to solve a second order ODE numerically. Let's say $y''+ay'+by =f(x)$ for ...
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### Derive implicit method from Butcher tableau

\begin{align*} \begin{array}{c|cc} 0 &0 &0 \\ 1 & \frac{1}{2} & \frac{1}{2} \\ \hline & \frac{1}{2} & \frac{1}{2} \end{array} \end{...
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### FEM for non linear PDEs

I am looking for an easy but rigorous reference for FEM methods for non linear PDEs like the p-laplace equattion or non linear heat equation ect. Can one recommend me a good exposition of this topic ...
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1 vote
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### Numerical method,how to do it? [closed]

Let $f(x)=x^4-x^2+17x+1$. Let $p\in\mathcal{P}_{20}$ interpolates f at $x_j=2^j(j=0,...,20)$,Compute $p(0)$
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### Which root does the bisection method prefer in case of multiple roots existing in the given interval?

Let $f$ be a continuous function over the interval $[a, b]$ such that $f(a)f(b) \leq 0$. Suppose $f(x)=0$ has greater than $1$ root in this interval. Which root does the bisection method eventually ...
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### How to transform this expression to a numerically stable form?

I have this function $$f(x, t)=\frac{\left(1+x\right)^{1-t}-1}{1-t}$$ Where $x \ge 0$ and $t \ge 0$. I want to use it in neural network, and thus need it to be differentiable. While it has a ...
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### Help understanding how to apply IMEX methods to one-dimensional PDEs

I need to compute a solution of the following PDE: $$\frac{\partial u}{\partial t} + v \frac{\partial u}{\partial x} = 0$$ For didactic purposes, I need to use an IMEX method. The point is no one ever ...
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### Applications of highly oscillatory integrals

I was reading a series of articles on numerical integration of highly oscillatory functions, e.g., S. Olver, Numerical approximation of highly oscillatory integrals S. Xiang, H. Wang, Fast ...
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