Question regarding ode15s

Hello Everyone,

I'm simulating a system of stiff differential equations of the form using ode15s

Y'= (1./Vector1).*(Matrix1*Y+Matrix2*Y)
Z'= (1./Vector1).*(Matrix1*Z+Matrix2*Z) % the matrix diff eqn for each variable Y, Z is created in a for loop 

The vector Y,Z is of size ~1200 and the number of differential equations is ~2400

The total simulation time takes around 570s when

odeset('abstol', 1e-10, 'reltol', 1e-9)

is used for error settings and it reduces by 5 times when the default error settings are used.

I tried to use the profiler and the ode solver takes around 508 s (snapshot ).

I'd like to know if I can speed up the compute time taken by the ode solver. Could someone clarify if the ode solver calls BLAS functions for Matrix operations? I'm using version 2019b

I would be happy to share addional details if the problem explained above isn't clear enough.

[Ameer Hamza]

Have you tried ode45()?

[Deepa Maheshvare]

Hi, my equations are stiff so I tried using ode15s.

Answer 1

[Kiran Felix Robert]

Hi Deepa,

The ode15 solver is slow for your specific error tolerances when compared to the default setting because the constraints set by you (1e-10 & 1e-9) are more strict when compared to the default values(1e-3 & 1e-6) .

Please check the odeset documentation for the default values.

To improve the solver speed you can try the following

1. Increase the error tolerances ( say increase the tolerances to 1e-2 & 1e-3).
2. Provide the Jacobian explicitly using the ‘Jacobian’ parameter of the ‘odeset’

Kiran Felix Robert