# Questions tagged [stability]

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

180 questions
Filter by
Sorted by
Tagged with
73 views

83 views

### Stability of the Forward-Time Central Space method, section 9.3 in LeVeque

I am reading section 9.3 in Leveque about stability. The explanations are very short and brief so I am asking for some help to understand and elaborations. The result of the section is that for FTCS ...
137 views

### How do I apply BDF2 in a STRANG splitting

I have a 3D diffusion equation that I want to solve using a time splitting (2D+1D). Assume that $A$ is the 2D discrete diffusion operator and $B$ is the 1D discrete diffusion operator. I want to use a ...
89 views

### Positive feedback instability

I have two black boxes (representing some multi-physics but that does not matter), where box #1 takes some quantity T as input and produces some quantity P as output; and box #2 takes P as input and ...
47 views

### Comparison between stability and accuracy of various Finite Difference schemes

Im Analyzing the 1D convection equation (PDE) for stability, consistency, and accuracy. I know Both upwind schemes (explicit and implicit) show better stability with a higher number of waves for ...
51 views

### Stability plot of upward difference implicit time

I am analyzing the stability of 1D convection (advection) equation as shown in the picture. When I derive the equations as shown I want to get rid of the complex number. Im asking if those stability ...
107 views

### Accuracy gap for apparently stable solution

I was reasoning about the behaviour of the methods I'm using for my simulation and I noticed that, considering $h_s$ as the timestep over which I have unstable solutions and $h_a$ as the timestep ...
123 views

### Exponent log to compute reciprocal power?

A MATLAB library seems to overcomplicate a computation: exp( (log(a) - log(b))/b ) which is mathematically equivalent (assuming real & positive ...
78 views

### Technique to find the CFL condition using the Galerkin method in space and finite-difference in time?

I am using the Galerkin method (Discontinuous to be precise) to discretize in space the scalar linear wave equation and the explicit second order centered finite difference scheme to discretize in ...
172 views

### Using the BDF and RK4 methods to solve this coupled system of ODEs in C++

I'm trying to solve a system of ODEs using the BDF order 4 method. I find the first 3 points using RK4, then for the implicit part of the BDF, I use Newton-Raphson iteration. Unfortunately my solution ...
36 views

### Numerical stability of taking the mean of outputs from the simulation of a discrete stochastic dynamical system

I am writing a simulation for a discrete stochastic dynamical system. Since the simulation is stochastic, I need to run the simulation multiple times and then average the values of each timestep. I ...
213 views

66 views

35 views

### Convergent Finite Difference Scheme for Parabolic Equation

Consider the PDE $$u_t = b_{11}u_{xx} + 2b_{12}u_{xy} + b_{22}u_{yy},$$ where $b_{11}, b_{22} > 0$, and $b_{12}^2 < b_1b_2$. In Strikwerda's book, the ADI scehme \begin{align*} \left( 1 - \frac{...
42 views

268 views

### log-sum-exp trick for signed/complex numbers

I need to evaluate a sum of values that are on many different orders of magnitude in scale but might be signed. I’ve had great luck with the “log-sum-exp” trick for an unsigned version of my problem, ...
221 views

### Numerical stability in the product of many matrices

I have to calculate in numpy the matrix-product of many matrices (~400). Are there common practices to increase numerical stability? If this is relevant, the matrices are $300\times 300$ orthogonal ...
170 views

60 views

### Bounding error of float32 matrix multiplication

Some numerical debugging led me to the minimal example below. I'm observing relative error of 0.75 on individual elements. Is there a way to estimate/bound this error without resorting to higher ...
30 views

49 views

84 views

### Numerical Stability of a Generalized Spatial Discretization Scheme

After reading the matrix stability chapter (10) of Hirsch [1], I decided to dive in the reference list of the chapter. One of the papers [2], which is cited as reference shows an very interesting ...
89 views

### Stability of PDEs

I am currently trying to solve some PDEs with FiPy. At page 56, the manual mentions (https://www.ctcms.nist.gov/fipy/download/fipy-3.0.pdf). The largest stable timestep that can be taken for this ...