Save/use intermediate values on ode solver

I am doing a time integration of a system of ODEs using a stiff solver (ode15s). It is working, but I want to speed things up.

The system of equations is given in state space form:

function [dx] = fun(t,x,M,C,K,other_parameters)
    % Mx'' + Cx' + Kx = F(t)
    % BUNCH OF CALCULATIONS
    F = myfun(x,t);
    
    A = [zeros(n) eye(n) ; -M\K -M\C];
    b = M\F;
    
    dx = A*x + b
end

The trick part here is the forcing function F. It is highly nonlinear and depends on the x and t parameters. It uses the x parameters to solve a Poisson-type 2D equation (by the Finite Volume method). The force F is proportional to the Poisson equation solution.

function [F] = solveP()
    % initialize solution
    Phi = zeros(Ni,Nj);
    
    % solve iteratively
    % ...
    
    % calculate F
    F = sum(Phi(:)); % discrete integration over domain
end

Solving the Poisson equation by a iterative method requires an initial condition, which I set to zero (Phi=zeros(Ni,Nj)). I thought I could improve the speed of calculations by providing a better initial estimative of the ϕ field (a better initial condition would take faster to reach the sought answer). The optimal initial condition I can think (besides ) is the value of the ϕ field obtained in the previous iteration (the last step) of the ode solver (.

Bottom line is: how do I use/save intermediate values in the ode solution?

PS: I tried using the persistent variables, but that is not a good solution. The ode solver calculates the function in several points before advancing in time. The persistent variable saves the converged ϕ field every time the ode calls the odefun fun. That is not exactly what I want.

Answer 1

[Pan Zhao]

I have a similar problem. Did you manage to solve your problem?

[Thales]

Unfortunately, no.

The best I could come up with was to write my own integrator. Clearly, it is not as good as MATLAB's built-in ode, but I can return other variables in the function fun being integrated and use them in the time marching scheme.

[Pan Zhao]

@Thales Thank you for the update.