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by pineln
December 4th, 2024, 5:08 pm
Forum: Numerical Methods Forum
Topic: Numerical Methods for ODEs where all variables are Matrices
Replies: 10
Views: 1514

Re: Numerical Methods for ODEs where all variables are Matrices

Short update. After correcting sevral errors in the paper I have managed to replicate all of its output. Thank you for all your help.
by pineln
November 5th, 2024, 5:54 pm
Forum: Numerical Methods Forum
Topic: Numerical Methods for ODEs where all variables are Matrices
Replies: 10
Views: 1514

Re: Numerical Methods for ODEs where all variables are Matrices

After changing out my Euler scheme for scipy odeint I was still not seeing the same behaviour as Figure 2 (page 9) of the paper suggested so I began deriving the matrices shown on page 9 by hand and found a small error in the papers definition of matrix R_A. After correcting this I began to see the ...
by pineln
November 5th, 2024, 1:37 pm
Forum: Student Forum
Topic: Matrix Ordinary Differential Equation Incorrect Solution?
Replies: 0
Views: 1586

Matrix Ordinary Differential Equation Incorrect Solution?

I have been trying to derive expressions for dA/dt and dB/dt from the below equation(s) for some time now in order to try and replicate the results from a research paper. However, when I attempt to calculate A and B @ t = 0 using numerical methods my solution blows up wich seems to suggest that the ...
by pineln
October 18th, 2024, 2:29 pm
Forum: Numerical Methods Forum
Topic: Numerical Methods for ODEs where all variables are Matrices
Replies: 10
Views: 1514

Re: Numerical Methods for ODEs where all variables are Matrices

Thank you so much for all your help, I really appreciate it. I have validated my Euler scheme using the scipy odeint - so I must be making my error(s) elswhere.
by pineln
October 18th, 2024, 10:16 am
Forum: Numerical Methods Forum
Topic: Numerical Methods for ODEs where all variables are Matrices
Replies: 10
Views: 1514

Numerical Methods for ODEs where all variables are Matrices

I am currently trying to replicate the 'Numerical Results' section of the attached  paper for my own interest. My current sticking point is solving the below system of ODEs where all the variables are matrecies:  \begin{equation} A'(t)=A(t)M^A A(t)+A(t)U^A+(U^A)^TA(t)+R^A\end{equation} \begin{equat...