How can I make my ODE system run faster

 options = odeset('mass',BigM,'MassSingular','no','BDF','on','MaxOrder',2,'Jacobian',...
    @(t,u) MyJacobian(t,u,MM_params, RHS_params, mask));
 
 [time,u_sol] = ode15s(@(t,u) TGetRHS(t,u, MM_params, RHS_params, mask), 0:0.4:tspan, U_init, options);

I have a project in which the main bulk of the work is solving a huge ODE coupled system of size of the form:

where

The RHS is partitioned into the sum of a "fast scale" and "slow" scale component. This makes the system very stiff, hence I am using ode15s in MATLAB and I tried to make things as sparse as possible.

However, my code takes several hours to run, and I have been thinking about how to use parallel or gpu computing to speed things up. I have checked MATLAB documentation to see if Ode15s can be solved on GPU, but I havent found any good answer.

I will appreciate any suggestion on how to make my code run faster in MATLAB or using other external software.

Answer 1

[Sulaymon Eshkabilov]

Use a variable step solver instead of the fixed step, e.g.:

 options = odeset('mass',BigM,'MassSingular','no','BDF','on','MaxOrder',2,'Jacobian',...
    @(t,u) MyJacobian(t,u,MM_params, RHS_params, mask));
 
 [time,u_sol] = ode15s(@(t,u) TGetRHS(t,u, MM_params, RHS_params, mask), [0, tspan], U_init, options);
  % 0:0.4:tspan --> To avoid the fixed step of 0.4