Questions tagged [matlab]

Questions about the numerical programming language MATLAB.

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26
votes
4answers
9k views

Method for numerical integration of difficult oscillatory integral

I need to numerically evaluate the integral below: $$\int_0^\infty \mathrm{sinc}'(xr) r \sqrt{E(r)} dr$$ where $E(r) = r^4 (\lambda\sqrt{\kappa^2+r^2})^{-\nu-5/2} K_{-\nu-5/2}(\lambda\sqrt{\kappa^2+...
39
votes
4answers
32k views

How does the MATLAB backslash operator solve $Ax=b$ for square matrices?

I was comparing a few of my codes to "stock" MATLAB codes. I am surprised at the results. I ran a sample code (Sparse Matrix) ...
2
votes
1answer
2k views

How can I implement the implicit Euler method for a small nonlinear system of ODEs?

I am trying to solve a system of coupled ODEs: $$ \begin{align} \frac{dn_A}{dt} & = e\left[j(t) - f\, θ_H\sinh\left(\frac{g\,n_A}{T}\right)\right] \\ \frac{dθ_H}{dt} & = a\left[bP\,(...
4
votes
4answers
7k views

Efficient assembly of finite element matrix in MATLAB

Question What is the most efficient algorithm for finding a row of a matrix which matches a given row? This is the same as a table lookup based on multiple criteria. Context Finite Element Matrices ...
6
votes
2answers
1k views

Projecting Finite Element solution onto new mesh

I am implementing a finite element solver in MATLAB and I have the following problem. Let's say I have a mesh $\mathcal{T}_1$ with triangular elements on a rectangular domain $\Omega\subset\mathbb{R}^...
4
votes
2answers
9k views

Visualising Maxwell's equations using MATLAB

I asked this question to help me understand what is going on in one of Maxwell's equations. I am happy with following through the maths on paper now, but would like to use MATLAB to take it one step ...
4
votes
2answers
288 views

Trying to model a simple second order ODE

I am studying some computational methods and I am trying to program simples equations to understand how the methods work... Particularly, I am trying to understand how multiorders ODE's work. I've ...
8
votes
0answers
648 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 ...
2
votes
1answer
2k views

3D Solid 8 Node FEM Matlab Code

So this semester, I'm taking a Finite Element Method course at my graduate school. We started out making codes for 1D bars and came all the way to 8 node solid elements. However, I seem to have run ...
1
vote
2answers
409 views

How to set up the differential equation system to speed up computation?

I've set up a system of differential equations, obtained after discretizing pde, in the following way ...
2
votes
1answer
3k views

Introduction to Lattice Boltzmann methods [closed]

I am trying to learn the Lattice-Boltzmann method and was looking for some good beginner resources explaining the method. I have been looking at some codes online, but have been having trouble ...
0
votes
0answers
2k views

Finite differences and Neumann boundary conditions

I am dealing with a highly nonlinear system of two PDEs. I already have a code to solve the system in case of Dirichlet boundary conditions. The explicit system is: $$ \begin{eqnarray*} \partial_{t}u ...
2
votes
1answer
5k views

Plot a surface from data sets in MATLAB

I tried to plot a surface in MATLAB but, since it is the first time I had to do something like this, I need a confirmation on the process I followed because it is important for my project to plot the ...
2
votes
1answer
203 views

MATLAB's ode45 not dealing with initial conditions well [RESOLVED]

*Concern highlighted in yellow *Solution at bottom I have a differential equation to solve for the motion of an electron: $$ \frac{d^2v}{dt^2} = \frac{1}{\gamma^6}\left( \frac{eE}{\tau m} - \left( \...
2
votes
1answer
670 views

Crank-Nicolson algorithm for coupled PDEs

Assumed I have the following two coupled equations $$\begin{split} \partial_tA&=a_0AB\\ \partial_tB&=b_0AB \end{split} $$ but I am not sure how to calculate them. One approach is a crank-...
1
vote
0answers
202 views

Oscillating convergence in my Resilient BackPropagation (RPROP) implementation

I have implemented in matlab a neural network that uses rprop's algorithm to update its weights. Strangely the error on the training set does not converge to a local minimum, but oscillates. Here is ...
1
vote
1answer
98 views

Integrating a function and then plotting it's graph in Matlab

I've been working on this code for some hours and it seems I'm doing something wrong which I just can't figure out. I have a function which I integrate and then plot it's values. But the graph I get ...
12
votes
2answers
3k views

What is the corresponding LAPACK function behind Matlab [Q,R,E]=qr(A)?

I currently trying to cheaply compute a good rank estimate for a matrix $A$. Therefore I compute a columnt pivoting QR decompostion using [Q,R,E]=qr(A) in ...
11
votes
3answers
1k views

Least squares approximation question

I am taking a course on scientific computation, and we just went over least squares approximation. My question is specifically about approximating using polynomials. I understand that if you have n+1 ...
9
votes
4answers
5k views

Order of MATLAB FFT frequencies

This wikibook states that the output of MATLAB's FFT corresponds with the wavenumbers ordered as: $$k=\left\{0,1,...,\frac{n}{2},-\frac{n}{2}+1,-\frac{n}{2}+2,...,-...
3
votes
2answers
374 views

Why iterative method: AMG preconditioned PCG is slower than Matlab direct method 'A\b'?

Recently, I have met a question that a saying goes that for large linear system: iterative methods are required because of memory problem of direct methods. But when I implement some experiments ...
10
votes
6answers
1k views

Soft Question: Where does Python fit into the picture?

So I've been debating whether or not I should bother learning Python. From speaking with my professors, Matlab seems to be the common language used in applied mathematics/computational science as far ...
8
votes
1answer
10k views

Matlab solution for implicit finite difference heat equation with kinetic reactions

I am trying to model heat conduction within a wood cylinder using implicit finite difference methods. The general heat equation that I'm using for cylindrical and spherical shapes is: Where p is the ...
5
votes
2answers
175 views

Effect of mesh size on solution curves for a 1D problem

I'm interested in studying the effect of mesh size on the behavior of the solution curves of 1D convection-diffusion problem. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - ...
4
votes
2answers
23k views

How to find all roots of equation in Matlab?

How to find all roots of an equation in Matlab? I tried and it gave me just one of the roots. For example: my equation is $F(x)=0$ where ...
3
votes
1answer
2k views

How do I form the Chebyshev differentiation matrix in MATLAB?

I have some code that does exactly this, but I do not like to use things I do not understand. Here is the code ...
1
vote
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 ...
0
votes
1answer
565 views

Multi-domain 3D Geometries for MATLAB PDE Toolbox

In principle the PDE Toolbox in MATLAB can handle multi-domain 3D geometries as noted here. This feature and the associated function geometryfromMesh were introduced in MATLAB R2018a. The associated ...
8
votes
5answers
4k views

Minimizing $\mathrm{trace}(S)+\mathrm{trace}(S^{-2})$ using CVX

In Matlab, I would like to minimize the function $$f(S)=\mathrm{trace}(S)+\mathrm{trace}(S^{-2})$$ where $S \in \mathcal{M}_{m,m}$ is symmetric and positive definite, which is definitely a convex ...
7
votes
2answers
2k views

How do I solve a boundary value ODE in MATLAB?

Specifically, ode15i. I have ode15i solving a system of 5 first order implicit odes in 5 variables with an initial condition (made consistent by decic). It's great for what I need, except I need to ...
6
votes
1answer
590 views

Is there a faster method to compute the geometric series of a matrix?

I want to calculate the geometric series of a matrix $A$: $$S=I+A+A^2+\dots+A^n$$ and then apply to a vector $v$, $Sv$. I've done it in Matlab with a loop and I think it's quite efficient applying ...
5
votes
2answers
2k views

Matlab: Solving $u_t = f(u) u_{xx} + g(u) u_x + h(u) u$

I am trying to solve the following equation numerically: $$\dfrac{\partial u}{\partial t}=\dfrac 3 x\dfrac \partial{\partial x}\left(\sqrt x \frac \partial {\partial x}(\nu(u,u^2,\cdots,u^k)u\sqrt x)\...
5
votes
2answers
558 views

Specifying ode solver options to speed up compute time

I'm specifying the 'JPattern', sparsity_pattern in the ode options to speed up the compute time of my actual system. I am sharing a sample code below to show how I ...
3
votes
1answer
406 views

Question on how MATLAB's pdepe solver works

I'm solving the following 1D transport equation in MATLAB's pdepe solver. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\partial x}$$ At the inlet (left ...
3
votes
2answers
2k views

SVD of large block-hankel matrix

I am trying to do SVD of a large block-hankel matrix for model order reduction (Low rank approximation). However, I quickly run into memory issues in forming the large Block-Hankel matrix and CPU ...
3
votes
1answer
953 views

How to implement flexible gmres in matlab?

About the flexible GMRES (fgmres), we know that it is a variant of right preconditioned gmres. And the robust command gmres in matlab as follows: ...
2
votes
1answer
1k views

Implicit heat diffusion with kinetic reactions

I am using the implicit finite difference method to discretize the 1-D transient heat diffusion equation for solid spherical and cylindrical shapes: $$ \frac{1}{\alpha}\frac{\partial T}{\partial t} = ...
2
votes
1answer
1k views

Numerical method for a BVP with mixed boundary conditions (MATLAB)

I've been given a second-order non-linear ODE: $$\frac{d^{2}\theta(s)}{ds^{2}} = sf_{g}\cos{\theta} + sf_{x}\cos{\phi}\sin{\theta}$$ where $f_{g}, f_{x}$ and $\phi$ are constants. The boundary ...
1
vote
0answers
2k views

How to solve an ode with stochastic time-dependent input

I am trying to repeat an example I found in a paper. I have to solve this ODE: $25 \ddot{x} + 15 \dot{x} + 330000 x = p(t)$ where $p(t)$ is a white noise sequence band-limited into the 10-25 Hz ...
0
votes
0answers
73 views

Comparison of diffusion time - theoretical value vs computed

This is a follow up to my previous post I've been trying to compare the diffusion time obtained from theoretical derivation(answered in my previous post) and what is obtained computationally, for a ...
0
votes
2answers
3k views

FEM Stiffness Matrix is always close to Singular or Badly Scaled

I am making a code for an 18-node (3x3x2) 3D element FEM. However, even though I am (pretty) sure that all the shape functions are correct and whatnot, whenever I try and invert the stiffness matrix ...
0
votes
1answer
519 views

How to simulate thermal expansion in a 2D plane using FEA?

I am trying to model 2D thermal expansion of a square area inside another square using FEATool. I have simulated plane strain by incorporating forces pointing along the $[1 \,\,\, -1]^T$ direction ...
0
votes
1answer
2k views

Solving Time dependent Schrodinger equation using MATLAB ode45 [closed]

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ I try to implement solve the Schrodinger equation for time-dependent Hamiltonian in ODE ...
0
votes
1answer
250 views

Nice plot of f(x)

A user has this nice graph of f(x) on his profile and I want to learn how to do it in matlab or Gnu octave. ...
0
votes
1answer
58 views

(2) Trying to model a simple second order ODE: Why time-step smaller is not better

This question is related with this other question: Trying to model a simple second order ODE. On this other question, I get some useful comments on why the simulations are so terrible. However, I have ...
12
votes
3answers
4k views

Choice of step size using ODEs in matlab

Hey there and thanks for giving time to look at my question. This is a updated version of my question which I posted earlier in physics.stackexchange.com I'm currently studying a 2D exciton spinor ...
9
votes
1answer
659 views

Matrix Balancing Algorithm

I have been writing a control system toolbox from scratch and purely in Python3 (shameless plug : harold ). From my past research, I have always complaints about ...
6
votes
2answers
1k views

matlab eigs: wrong eigenvalues for tridiagonal matrix

I try to compute eigenvalues of the tridiagonal matrix coming from finite difference scheme. For small mesh size, eigs works well. But for large size it fails. Here is an example where eigs fails. Is ...
5
votes
3answers
354 views

PRIMA gives an unstable result?

I am working with Modified Nodal Admittance representation of circuits. I am doing Model Order Reduction using PRIMA on MATLAB. I am considering these circuits as Descriptor State-Space systems. I ...
4
votes
1answer
1k views

How to find conditional Lyapunov exponents

For a synchronized ODE system,I wanted to know if there is a program code in MATLAB available for plotting the conditional Lyapunov exponent. For example, synchronization of identical Rossler system ...