How do I use ode45 for descriptive form?

What would be the most efficient way to solve,

A1x'(t) = A2x(t), where both A1 and A2 are nxn matrices.

Both are sparse matrices and hence I want to avoid inversion.

Answer 1

[Yu Jiang]

You may solve it as a DAE (differential algebraic equation), instead of an ODE.

This documentation (Link) mentions the DAE in the form of

M(t,y)y′ = f(t,y)

Your example is a special case of this form. It can be solved by ode15s and ode23t solvers. Using those solvers, you can directly specify the M matrix without the need to invert it.

Basically, you define a function as

function dx = mySys(t,x)
  dx = A2*x;
end

Then, before you solve it using ode solvers ode15s and ode23t, specify

options = odeset('Mass',A1);

Next, apply the option when using the solver as follows

[t,y] = ode15s(@mySys,tspan,y0,options);

More examples can be found in the documentation .

[Tawsif Khan]

Any reason why it is restricted to the use of ode15s and ode23t only?

[Yu Jiang]

I think it is because they use different numerical methods. See the following link for details:

http://www.mathworks.com/help/matlab/ref/ode15s.html#f92-998740

-Yu

[Tawsif Khan]

Thanks, this really helped.