# Tagged Questions

A method in numerical analysis which consists of approximating the derivatives of a solution of an ordinary or a partial differential equation. This leads to the solution of a linear system.

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### Show that there is an equilibrium point

Show that if $x_{k+1}=f(x_{k})$, where $f$ is continuous, has two stable equilibrium points, then there's a third equilibrium point between then. I'm trying to approach this problem using the ...
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Now I have $f : \mathbf{R}_{+} \rightarrow \mathbf{R}$ be defined as $f(k_{t}) = \frac{k_{t}}{\alpha + (1-\alpha)k_{t}}$ $p_{t+1} = \frac{r}{n}p_{t} + \frac{\beta}{n}k_t + \frac{(e+s-1)}{n}f(k_{t}... 0answers 17 views ### Finite difference along a line of$xyz$coordinates I have a line of$x,y,z$coordinates. I'm looking at using finite differences in order to find local maxima (of$z$)..i.e. 'hills'. Am I right in thinking that I can use the second derivative? I have ... 1answer 34 views ### accurate vibration analysis (finding eigenvalues) of a large, sparse, non-symmetric matrix I have a large, sparse, non-symmetric matrix$M$, and I need to get accurate eigenvalues$\lambda_i$and eigenvectors$\vec{s}_i$for all$i\$. (An example system is below; it's based on a finite-...
$$\frac{\partial\phi(\mathbf{x},t)}{\partial t}=g(\mathbf{x})(\varepsilon^{2}\Delta\phi-F^{'}(\phi)),\ \ \ \mathbf{x}\in \Omega,t>0\ \ (*)$$ \frac{\...