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Hi Guys
Posting this based on a thought I had, so I don't really ahve any code however I would like to know if the thought process is correct and/or relatively accurate.
Consider a simple spring mass system which only allows compression on the spring however when there is tension the mass should move without the effect of the spring distrupting it, thus the mass is just thrown vertically upwards.
The idea which I came up with for such a system is to have two sets of dfferential equations, one which represents the spring system and another which presents a mass in motion without the effects of the spring.
Please refer to the below basic outline of the code which I am proposing. I believe that this may produce relatively decent results. The code essentially checks if there is tension in the system if there is it then takes the last values from the spring mass differential equation and uses it as initial conditions for the differential equation with the mass moving wothout the effects of the spring, this process works in reverse also. The error which would exist is that the initial conditions applied to the system would include effects of the spring. Would there be a better way to code such behaviour?
function xp = statespace(t,x,f,c,k,m)
if (k*x(1)) positive #implying tension
**Use last time step as initial conditions**
**differential equation of a mass moving""
end
if x(1) negative #implying that the mass in now moving down therefore compression in spring
**Use last time step as initial conditions**
**differential equation for a spring mass system**
end
end
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The way we've solved ODEs in MATLAB has been relatively unchanged at the user-level for decades. Indeed, I consider ode45 to be as iconic as backslash! There have been a few new solvers in recent years -- ode78 and ode89 for example -- and various things have gotten much faster but if you learned how to solve ODEs in MATLAB in 1997 then your knowledge is still applicable today.
In R2023b, there's a completely new framework for solving ODEs and I love it! You might argue that I'm contractually obliged to love it since I'm a MathWorker but I can assure you this is the real thing!
I wrote it up in a tutorial style on The MATLAB Blog https://blogs.mathworks.com/matlab/2023/10/03/the-new-solution-framework-for-ordinary-differential-equations-odes-in-matlab-r2023b/
The new interface makes a lot of things a much easier to do. Its also setting us up for a future where we'll be able to do some very cool algorithmic stuff behind the scenes.
Let me know what you think of the new functionality and what you think MathWorks should be doing next in the area of ODEs.
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The new solution framework for Ordinary Differential Equations (ODEs) in MATLAB R2023b

Along with linear algebra, one of the iconic features of MATLAB in my mind is how it handles ordinary differential equations (ODEs). ODEs have been part of MATLAB almost since the very beginning.One of the features of how MATLAB traditionally allows users to solve ODEs is that it provides a suite of functions. For many years, there were 7

blogs.mathworks.com

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