How can I input an array into ode45?

I am trying to solve a 2nd order ODE using ODE45. I would like to input an array of different initial conditions such that it would output an array of solutions. How can I do so?

[KSSV]

Are you not okay with loop?

Answer 1

[Walter Roberson]

Assuming the initial conditions are columns of a matrix IC:

[T_vals, Y_vals] = arrayfun( @(idx) ode45(@odefunction, tspan, IC(:,IDX)), 1:size(IC,2), 'uniform', 0);

T_vals and Y_vals will be cell arrays. If your tspan is two elements instead of a vector of length 3, then you could have a different T_vals vector for every case; if your tspan is a vector of at least 3 elements, then the T_vals entries should be the same for each case unless the ode45 gives up because of a singularity or an event function.

This is a hidden loop; MATLAB will do the loop inside of arrayfun.

There is a more compact form for the special case where the initial condition is a scalar for each call:

[T_vals, Y_vals] = arrayfun( @(ic) ode45(@odefunction, tspan, ic), IC, 'uniform', 0);

Answer 2

[Nicolas Schmit]

You cannot directly input an array of initial conditions to ode45. It might be possible to define a function handle solveOne(y0) = @(y0) ode45(..., ..., y0) and apply this function to your array of initial conditions using arrayfun(solveOne, ...). However, you would not get better performances than with a for loop. Furthermore, the for loop can be easily replaced by a parfor if you have the Parallel Computing Toolbox.