Solve Semilinear DAE System

Hi there,

Here I have two questions. Firstly, I want to know, in the file “Solve Semilinear DAE System” of the help center,

The following codes to create the function handle suitable for input to ode15s or ode23s

M = @(t,Y) massM(t,Y,m,r,g);

F = @(t,Y) f(t,Y,m,r,g);

I am not sure what Y is in these two lines. May I directly use the command functionhandle to create the mass matrix and the RHS of the ODE function?

BTW, what algorithms are used to generate the constraints from the code reduceDAEToODE?

Secondly, what is a semilinear DAE?

Many THX!

Answer 1

[Torsten]

I am not sure what Y is in these two lines.

Y is the (numerical) vector of unknowns - in the example Y = [x,y,T,dx/dt,dy/dt].

May I directly use the command functionhandle to create the mass matrix and the RHS of the ODE function?

I don't know what you mean. Is there a command "functionhandle" in MATLAB ?

BTW, what algorithms are used to generate the constraints from the code reduceDAEToODE?

I think TMW won't tell because it's intellectual property.

Secondly, what is a semilinear DAE?

I think it's a system of differential and algebraic equations that depends only linearly on the derivatives. That means it can be written in the form

M(t,Y)*dY/dt = f(t,Y)

with a matrix M that can depend on t and the vector of unknowns Y.

This is in contrast to a fully-implicit DAE system which is of the form f(t,Y,dY/dt) = 0. Here, dY/dt could enter the DAE-system in any form, e.g. (dY/dt)^2, sin(dY/dt) or similar.