# linear 1st order ODEs sytem with time-dependent coefficients solver

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I need to solve many times the following ODEs system:

F'(t) = A(t)*F(t) + B(t)*U(t)

F(0) = F0

where matrices A(t), B(t) and vector control function U(t) contains time-dependent coefficients or functions, which are represented in my case by discrete time-series (fixed sampling period ~ 1sec, 1e3-1e5 samples). Typical dimension of problem is ~ 2 - 6.

Proper interpolation (smooth and fast enough) of discrete time-series is the crucial requirement.

This ODEs systems will be solved many times (~ 1e2-1e4 times) for different A(t),B(t), U(t) and F0 , so solver should be fast enough + parallelizеd (multithreaded).

The MATLAB offers a set of generic ODE solvers, but I am looking for a specific problem solver (linear 1st order ODEs system with time-dependent coefficients), which will be fast and reliable. So far I found only one solver - LDE.

My questions are:

- Is there any other special solver (implemented in MATLAB) suitable to solve my specific problem effectively and reliably?
- Is there any reason to expect, that some special solver would be better than standard MATLAB ODE solvers in my specific problem?
- Is there any suitable or recomended strategy how to solve this specific problem?

##### 12 Comments

Bjorn Gustavsson
on 3 Aug 2023

### Accepted Answer

### More Answers (1)

Michal
on 25 Jul 2023

Edited: Michal
on 25 Jul 2023

##### 5 Comments

Paul
on 25 Jul 2023

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