# Questions tagged [stability]

The study of the propagation of errors in a numerical algorithm.

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### Boundary value problem solver fails on trivial case

I am trying to solve a boundary value problem on $[0, \infty]$, using scipy's scipy.integrate.solve_bvp and I am seeing that the solutions are not converging even ...
1 vote
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### How to classify ODE equilibria that are stable but slowly changing in value with time?

I'm numerically solving a system of coupled ODEs where time is the independent variable. At each time, I can solve for the equilibrium values of my state variables where their respective derivatives ...
139 views

### Should reaction be taken into account in the CFL condition when solving advection-diffusion-reaction equations numerically?

I'm dealing with the numerical resolution of advection-diffusion-reaction equations. I've encountered references on CFL conditions for conservation laws as well as advection-diffusion equations. I'm ...
1 vote
68 views

### stability of a numercial scheme for a hyperbolic system?

This is related to my question here https://math.stackexchange.com/questions/4447383/lax-wendroff-scheme-stability-analysis-for-a-linear-system-of-conservation-laws . Consider the numerical scheme ...
81 views

### Numerical algorithms made stable by unums which are unstable on IEEE floats

For unums, there is good evidence (see figure 5) that accuracy is better than IEEE floats. (Note: I use the term "unum" broadly to refer to any of the various iterations and revisions to the ...
88 views

### How to estimate stability and stiffness of a system of coupled ODEs?

I'm running into issues with Python/Julia ODE solvers requiring prohibitively small timesteps to evolve a system of 4 coupled ODEs (the order of magnitude of the state variables and time unit span ~40-...
195 views

### Numerical instability in the inverse Laplace transform

I have a problem with Laplace inversion and my function is not numerically stable for the Laplace inverse, but I do not understand the cause of this problem. Here is my code and graph of this problem. ...
1 vote
42 views

### Generate numerically stable equation automatically

I remember there is a software (and its website interface) that can generate numerically stable equation from an expression automatically. To see the problem it tries to solve, let’s take a look at a ...
59 views

### robust numerical calculation with large (almost) offsetting terms

I am attempting to evaluate an expression that defines a probability of a particular event. With 3 different events, I can (under some statistical assumptions) characterize the probability of event 1 (...
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129 views

### Floquet theory for periodic delay differential equations: current numerical routines

I would like to determine the stability of a system of periodic delay differential equations (a seasonal host-parasite model). I've tried to implement the method described in Lemma 2.5 in this paper: ...
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1 vote
156 views

### Finite Difference for Advection Equation With Source

I'm trying to find a convergent finite difference scheme for the PDE \begin{equation} \begin{split} u_t + (x-1) u_x &= (x-1)u, \hspace{.5cm} x \in [0,1] \\ u(x,0) &= 1 \\ u(1,t) &= 1. \\ \...
I currently have a code that solves $u_t+ cu_x=0$ with periodic boundary conditions, and constant $c$ (using an upwind method). I'm wondering how I would alter this code to solve something of the form ...