# Questions tagged [convergence]

Questions related to whether the sequence of iterates generated by an iterative method has one or more limit points, and if those limit points have the correct properties.

187 questions
Filter by
Sorted by
Tagged with
2answers
667 views

### Implementing Gelfand’s formula for the spectral radius in Python - lack of convergence

For context: Gelfand's formula for the spectral radius is $\lim_{k\rightarrow \infty}|A^k|^{1/k}$ where $|\cdot|$ is any well-defined operator norm. I naively coded a function to calculate the $k$th ...
1answer
132 views

### Interpreting convergence study results, fixed CFL

I am trying to determine the order of my numerical method for resolving a fluid-structure interaction problem using the immersed boundary method. I am using Crank-Nicolson to resolve the fluid ...
1answer
195 views

### Problem with Richardson extrapolation method for weak convergence in SDE

I have implemented the Richardson extrapolation of the Euler-Maruyama method to 4th order, to estimate the moments of SDE. The Euler-Maruyama works, and I would expect the Richardson extrapolation to ...
1answer
997 views

### Error norm in finite difference calculation

I've used an explicit finite difference scheme to model the 1D time dependent temperature distribution in a friction weld. I want to now verify the consistency and convergence of my algorithm. I have ...
1answer
200 views

### Root Convergence rate of Iterative Scheme

I have an iterative sequence for optimizing an EM (Expectation Maximization) algorithm based loss function $L(X)$ with $t$ being the iteration number as: $X_t=ABX_{t-1}+CX_{t-1}+X_{t-1}$ where $A$ is ...
1answer
234 views

### Number of GMRES iterations increase when stepping forward in time, using the Newton method

I am solving a system of nonlinear time-dependent equations using the Newton method in a finite-element-setting, i.e. first I create the jacobian matrix for the current time, and afterwards I try to ...
1answer
131 views

### Blowup of error in Conjugate Gradient method with periodic Dirichlet Poisson matrix

My problem is that the L2-Norm of the residual for the periodic Poisson matrix $P$ is initially decreasing but starts to blow up after a certain number of iterations. The blowup happens earlier the ...
1answer
1k views

0answers
637 views

### Does applying the Newton-Raphson iteration for matrix reciprocal refine a matrix inverse from LU/GE?

This is a follow-up to this answer. Suppose you have a possibly very ill-conditioned matrix $A$, and you compute its inverse with LU/GE to get $X_{\text{lu}}\approx A^{-1}$. The Newton-Raphson ...
0answers
111 views

### Strange convergence behavior of WENO5 for Hamilton--Jacobi equations

I have the following question. I have a code function that computes right-biased and left-biased approximations of the derivative of a function using WENO5 for Hamilton--Jacobi equations as described ...
0answers
69 views

### Dynamic Successive Over/under Relaxation (SOR) with several variables

I am solving a partial differential algebraic equation (PDAE) system which has the following dependent variables: $f=f(X,T)$ and $g=g(T)$, along with a few others My current method for coupling is ...
0answers
965 views

### Newton Iteration method convergence

I wrote a Python code which solves a second degree nonlinear differential equation using the Newton iteration method. The code converges to a 2-cycle within 50 or so iterations. The cycle only ...
3answers
870 views

### necessary and sufficient tests to show order of convergence for the numerical method

I would like to know what are the necessary and sufficient tests one has to perform in order to show the convergence of the algorithm. I have not found a good reference to state for that as I am ...
2answers
123 views

### First-order ODE scheme implementation giving less than first-order convergence?

I am solving the initial value problem $$\frac{d}{dt} (E C_g) = -\delta, \quad E(0) = E_0,$$ for $E$, where $E$ and $C_g$ are functions of $t$, $C_g$ is completely known, and $\delta$ is a function ...
2answers
2k views

### Finding rate of convergence by curve fitting in Matlab

I have some data: number of nodes $N$ and error in energy norm corresponing to it. I have seen in some references that the rate of convergence is reported by $$\| u-u_h\| _E=CN^{\alpha}$$ How can ...
2answers
358 views

### Does the convergence of finite element have limit?

I have been trying to solve a nonlinear PDE related to structural mechanics (nonlinear Timoshenko beam to be precise). I am doing both h-refinement and p-refinement to reach the solution. The ...
1answer
118 views

### Step3 in deal.II - Convergence of the mean

I'm trying to understand the Convergence of the mean part of the Step-3 tutorial in deal.II. The authors say that $\frac{1}{|\Omega|}\int_{\Omega} u_h(x)dx$ converges with $\mathcal{O}(h^2)$, but I ...
3answers
126 views

### Guess the final term of a converging series [closed]

I have a non-linear equation that converges, and reaches suitable accuracy after around 20 steps, however each step is very expensive to calculate. The series are never quite the same, but they are ...
1answer
80 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. \\ \...
2answers
106 views

### Relationship between global and local error?

In some cases I have seen that if the local error is: $Err = O (\Delta t^{p+1})$ where the global error is p. So if local error is 3, global will be 2. Does somebody know where it comes? For ...
1answer
389 views

### Problem with convergence of Jacobi iterative algorithm

I'm dealing with Jacobi iterative method for solving sparse system of linear equations. For small matrices it works well and gives right answers even if matrix is not strictly diagonal dominant, ...
1answer
73 views

### Issue solving nonlinear equation containing a quotient

I have a coupled set of PDEs that need to be solved as part of a larger problem. I am currently approaching this by computing spatial derivatives with finite differences and using PETSc's nonlinear ...
1answer
293 views

### what is non-asymptotic convergence?

I guess convergence in general means it is in asymptotic sense but what does non-asymptotic convergence mean?. Can someone please explain with an example?
1answer
93 views

0answers
52 views

### Decrease in slope during convergence analysis

I am using the method of manufactured solutions to perform the order of accuracy testing. I am using a cube for the testing. The cube is size 1m on all sides. I used 5 refinements: \$dx = dy = dz = ...
0answers
63 views

### BFGS convergence problem

I would like first to state that it is beyond my capability to identify whether this is a BFGS issue or a R package problem. I've been doing some mixed logit regression using the R package "mlogit". ...
0answers
78 views

### Successive iteration method for solving eigenvalue ploblem

I have a question concerning the branch of successive iteration methods (Newton, Runge-Kutta). I definitely know (or can read in Wikipedia) the implementation of these methods. But I was wondering ...
0answers
238 views

### Accuracy of finite difference method for heat equation on a disk

To study an approximation for the heat equation $$\frac{\partial^2 u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}+\frac{1}{r^2}\frac{\partial^2 u}{\partial\theta^2}=f(r,\theta)$$ on the ...