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Questions tagged [matlab]

Questions about the numerical programming language MATLAB.

7
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0answers
453 views

Numerical implementation of the Dirichlet-to-Neumann map

I am solving the Dirichlet problem $$ \begin{cases} \Delta u = 0, \\ u|_{\partial D} = f, \end{cases} $$ in a $2d$ domain $D$ using the finite element method. What I want to get is the ...
7
votes
0answers
142 views

Tucker factorisation to compare multiple PCA decompositions?

This is an entry-level question for multiway matrix decompositions. I have a set/population $k$ of entities (here biological cells) for each of which I also have a number ($l$) of flavours of length $...
6
votes
0answers
165 views

Find the solution of linear equation using Wiedemann/ Krylov method

Let given $M =$ 1 0 1 0 1 1 1 1 1 and $b =$ 1 0 1 How to find the solution $x_3$ where $x=${$...
4
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0answers
68 views

MATLAB: Compute the Schwarz-Christoffel transformation symbolically

Suppose we have a conformal mapping from the unit disk in the $\omega$ plane onto the exterior of a polygon in the $z$ plane. The Schwarz-Christoffel mapping in this case is defined as: $$f(u) = A - ...
4
votes
0answers
66 views

Complex Integral Equation Solution in MATLAB

I need to solve an integral equation in the form: $$A(z)+\int\limits^{z_2}_{z_1}B(z') \frac{z^N}{z^N-z'^N} \frac{e^{i\beta}}{|z|}\mathrm{d}z'=0 $$ where $A(z)$ distribution is known and we are ...
4
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0answers
144 views

Galerkin FEM error when using even number of elements

Intro: I am developing a Galerkin FEM code in matlab - starting small with a simple 1D ODE. The equation I'm trying to solve is: $$a u_x = cos(x), x \in [0, 2\pi]$$ Which has a known exact solution $$...
4
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805 views

2D wave equation with Mur boundary condition - setting up the RHS and solving (time-steps)

I am trying to solve a 2D wave equation implicitly using FD with central approximations with the following boundary conditions $$\begin{align} &u=2\sin\left(\frac{2\pi}{5}t\right)\quad \text{at }...
3
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0answers
103 views

Iteratively solving a sparse, ill-conditioned system

I have a sparse (density = 0.2%), ill-conditioned system that I am trying to solve, with no luck. Background I have a sequence of sampled data, where two of every 8 samples have been zeroed due to a ...
3
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0answers
111 views

Methods to implement floor dirt detection algorithm

I'm trying to detect dirty floor areas in a series of images, using MATLAB and its Image Processing Toolbox, like the one that follows: In the image above, there are two distinct areas, the whiter ...
3
votes
0answers
241 views

MATLAB: solving multiple ODE systems in parallel

I have a system of parameterized ODEs that I would like to solve using MATLAB and its ode45 solver, and was wondering if it is possible to perform such a task in ...
3
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0answers
183 views

Numerically solving a system of partial integro-differential equations in Matlab

Given the following system of partial integro-differential equations $$ \frac{dX(t)}{dt}=\Lambda-\mu X(t)-\beta X(t)Z(t),\\ \frac{\partial Y(t,\omega)}{\partial t}+\frac{\partial Y(t,\omega)}{\partial ...
3
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331 views

C60 orbital calculation

I am currently trying to reproduce the results published by Hands et al.1 using MATLAB. They calculated the bases of the C60 wave functions of HOMO, LUMO and LUMO+1. I did the following: I ...
3
votes
0answers
355 views

Calculate Integral Using Gauss Jacobi Quadrature or otherwise

I need to integrate the following integral: \begin{align} I = \int^z\frac{1-\zeta^2}{(1+\zeta^2)(\zeta-\zeta_l)(1-\zeta_l\zeta)}\prod_{k=2}^{n-1}\left ( \frac{\zeta-z_k}{1-\zeta z_k} \right )^{-\...
3
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0answers
3k views

Numerical integration and filtering of acceleration experimental data

I have a vector containing acceleration measurements and the corresponding vector of times in which measurements are taken. To obtain velocity and displacement I used the cumtrapz() function already ...
3
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0answers
288 views

Efficient assembly of finite element matrix(coupled equations case)

I noticed this post, where spalloc and sparse are recommanded for efficient assembly in Matlab. I personally use sparse assembling for simple cases. However, when it comes to the case of coupled PDE, ...
3
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0answers
112 views

Spatio-temopral wavelet analysis

Am quite new to wavelet analysis and would like some help. I am performing a spatio-temporal analysis of monthly gridded rainfall data. With PCA, I can reduce the dimension of the rainfall data into a ...
3
votes
0answers
356 views

Transport Equation in a Tube: Source Term on Boundary

I'm modeling mass transport in a flow reactor. The flow reactor is a tube, which allows me to use cylindrical symmetry in solving the Convection-Diffusion-Reaction (CDR) Equation, which governs the ...
2
votes
0answers
28 views

ILUTP in sparse.linalg.spilu?

In Matlab, an ILU with threshold and pivoting (ILUTP) can be passed by default as: setup.type = 'ilutp'; [L, U] = ilu(A, setup); Looking for an equivalent in ...
2
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0answers
55 views

Unusual boundary conditions on Matlab

I'm trying to solve the following PDE by Matlab, $$ u_t-\Delta u = 0, \quad \text{in}\quad \Omega\times (0,T) \tag{1} $$ $$ u_t-\Delta_\Gamma u + \partial_\nu u=0,\quad \text{on}\quad \Gamma\times(0,...
2
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0answers
51 views

How to find two points within defined region in this constrained optimization problem?

I am doing a project related to robotics where I am using fmincon function from matlab to minimize the distance between the points ...
2
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0answers
92 views

What is Chebfun `eigs` doing

What is this doing? Looks like the original eigenvalue problem is converted into generalized eigenvalue problems with different dimensions of collocation points. Can someone explain more about this? ...
2
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0answers
89 views

Precision not improving by decreasing step-size in nonlinear Schrödinger

I tried to simulate soliton propagation by solving the nonlinear Schrödinger equation using the split-step Fourier method. The following is an example of the Matlab code copied from a textbook. ...
2
votes
0answers
169 views

Modeling First Order Parabolic PDE (Battery Storage Model)

I'm trying to solve the following first order parabolic partial differential equation, \begin{equation*} X \frac{\partial V}{ \partial Q} = -\frac{1}{2} \sigma^2 \frac{\partial^2 V}{\partial X^2} + ...
2
votes
0answers
208 views

ODE events to switch between 5 equations (friction model)

I am modelling a 1 dof spring-mass-damper system with friction. As first attempt I modelled the friction according to the simple Coulomb model (figure A here http://article.sapub.org/image/10.5923.j....
2
votes
0answers
303 views

Solving constrained BVP, singular Jacobian

The boundary value problem is $$ \begin{cases} \dot{x}_i = \begin{cases} (0.5D^{-1}\psi)_i, \text{ if }(0.5D^{-1}\psi)_i \le 0 \\ 0 \text{, otherwise} \end{cases} \\ \dot{\psi} = 2\Sigma x \\ x(0) =...
2
votes
0answers
43 views

Constructing 2 fold oversampled cosine basis in MATLAB

So I'm trying to construct a 2 fold oversampled cosine basis in MATLAB. I know how to construct the basis as a square matrix using the following command: ...
2
votes
0answers
299 views

Arpack and Matlab give different values for eigenvalues

I am solving a generalized eigenvalues problem with inversed complex shift: $$(M-\sigma J)^{-1}J \boldsymbol{x} = \boldsymbol{x} \nu \enspace .$$ My matrices are obtained from a finite element ...
2
votes
0answers
155 views

Using Centroid decomposition instead of SVD

This paper says centroid decomposition (CD) is an approximation to singular value decomposition (SVD). First I do not understand CD yet, since code is available I just want to try it out how it works ...
2
votes
0answers
216 views

1 D Diffusion equation FDM with different layers

I'm trying to solve this particular equation $\frac{\partial u}{\partial t} = \frac{\partial}{\partial x} \big[D_{i}(x)\frac{\partial u}{\partial x} \big] + S(x,t)$ where the $i$ index denotes ...
2
votes
0answers
83 views

Bracket Algebra, Straightening Algorithm

My apologies if the question is simple. I need to write a code for straightening algorithm. Which includes defining bracket algebra. I tried to write it in CoCoA-5, but it wasn't possible because ...
2
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0answers
279 views

ARPACK gives different answers from Matlab and NAG

I'm playing with ARPACK. I looked into the examples they provide, zndrv4.f illustrating the usage of the routine znaupd, in the directory of ARPACK/EXAMPLES/COMPLEX/. I also came cross NAG Fortran ...
2
votes
0answers
1k views

Self-consistent numerical solution of a set of equations

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} -\frac{\hbar^{2}}...
2
votes
0answers
98 views

Preconditioner for large size hermitian eigenvalue problems

Basically I try to compute several smallest eigenvalues of some sparse 50k*50k eigenvalue problems using matlab. $$Ax = \lambda Bx$$ With matlab eigs, it's not as fast as I expected. So I tried some ...
1
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0answers
40 views

Computing Trajectory Equations of Kerr Geodesics

I want to numerically solve the trajectory equations of a Kerr geodesic given by wikipedia in Matlab. The trajectories look like: I implemented the equations and solved it with the standard Runge-...
1
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0answers
112 views

High-accuracy numerical differentiation

I have a $200 \times 200$ matrix representing the values taken by a function over an equally spaced grid. I would like to perform derivatives on it. I am interested in its gradient (i.e. its ...
1
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0answers
16 views

Translating grid with extrusion speed

I am putting into MATLAB code the equations that describe a plastic extrusion process. From a paper, I found I should use a spatial grid that translates with the extrusion speed, being the reference ...
1
vote
0answers
97 views

Finite differences for the one-phase Stefan problem

I am trying to code the one-phase, one-dimensional Stefan problem using finite differences in Matlab, similarly to what has already been done in Mathematica (see https://mathematica.stackexchange.com/...
1
vote
0answers
55 views

scaling in discretized PDE system

I want to solve the following system via Matlab $\Omega=(0,1)^2$ $$\Delta y=\frac{1}{\alpha} p$$ $$ -\Delta p= y -1 $$ $$p|_{\partial \Omega}=0,~y|_{\partial \Omega}=0$$ using ...
1
vote
0answers
97 views

Band structure of nonlinear Schrodinger equation with one dimensional potential

I have a nonlinear Schrodinger equation which reads: $$ \frac{1}{2} \frac{d^2u}{dx^2}+ |u|^2u + V(x)u = -i \frac{du}{dz},$$ where $V(x)=\cos(wx)+ i a \sin(wx)$ and $w$, $a$ are numbers. How to ...
1
vote
0answers
44 views

Discrepancy in estimating boundary stencil for finite difference method

I am trying to estimate the FD stencil for boundary as mentioned in this paper (section 4.1) using MATLAB. The stencil order (6th) is higher than the one mentioned in paper (4th). $$ f_1' +\alpha f_2'...
1
vote
0answers
306 views

Vectorizing Matrix Multiplication

I would like to do the following operation: I have a "4D" matrix A and a "3D" matrix B. Both A and B are actually 2D matrices, where for A, each element is a 2D matrix, and for B, each element is a 1D ...
1
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0answers
33 views

Pseudo-Spectral cosine transform

I'm trying to solve the following equation $$u_t = u_{xx} + u(1-u^2), u_x(\pm 1) = 0,$$ using the Fourier cosine transform. The nonlinear term gives a convolution which I would rather avoid, which is ...
1
vote
0answers
125 views

Second Quantization in Matlab

This question may be more suited for physics.stackexchange, but I saw this post was recommended for StackOverflow or Computational Science, so I'm asking my question here. I am trying to write a ...
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vote
0answers
72 views

Approximating derivative of numerical solution (using ode45) within event function

The issue I have is having to compute the derivative (in real time) of the solution produced by ode45 within the events function. Some pseudo-code to explain what I'm mean is, ...
1
vote
0answers
153 views

Why can I not solve the negative advection equation (backwards in time)?

Suppose we have the negative, inhomogeneous advection equation: $$\left(\frac{\partial}{\partial x}-\frac{1}{c}\frac{\partial}{\partial t}\right)v(t,x)=u(t,x)\qquad(t\in\mathbb{R}_{+},x\in\mathbb{R})$$...
1
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0answers
148 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 ...
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0answers
368 views

How accurate is cumtrapz in MatLab?

Say I have a set of discrete acceleration data and want to integrate it to get a set of velocity data. How accurate is the cumtrapz (Cumulative trapezoidal ...
1
vote
0answers
82 views

Composite Laminate Mass Matrix Help

So, as the title of the post implies, I'm making an FEM code for a composite laminate plate using the Mindlin plate theory. And, as I am trying to get the mode shapes for the plate, I needed to make a ...
1
vote
0answers
143 views

Estimate $L_2$ norm of a elliptic problem with unknown exact solution on finite element method

I have the elliptic problem $$-\Delta u = 1,\,\,\Omega\subset\mathbb{R}^2$$ with $u=0$ on $\partial\Omega,$ with $\Omega=[-1,1]^2\backslash([0,1]\times[-1,0])$ and I want to estimate the $L_2$ error ...
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0answers
123 views

Eigenvalues using QR iteration

I'm trying find the eigenvalues of a matrix A using QR iteration with Householder. I used this code which I found from Cornell University that decomposes QR with Householder. ...