MATLAB: How to use ode45 for descriptive form

invertode45sparse

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.

Best Answer

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 .
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