Mixed precision explicit numerical methods for ordinary differential equations

Our objective is to solve large systems of ordinary differential equations (ODEs) commonly used to model biological processes.

These equations are typically nonlinear, complex, and high-dimensional.

In computational biology, such ODEs are generally solved using numerical methods.

In this work, we focus on explicit numerical methods because of their flexibility.

However, their limited stability regions may result in high computational costs.

To mitigate this issue, we investigate mixed precision algorithms designed to reduce computational effort by performing selected parts of the numerical method in lower arithmetic precision.

We develop several mixed precision explicit methods and assess their performance on two large scale biological benchmark ODE models.

Our theoretical analysis highlights the effectiveness of partially reducing arithmetic precision within explicit methods.

Numerical experiments demonstrate that our mixed methods-implemented in both sequential and parallel versions using MPI-combining single (float) and double precision arithmetic can achieve up to twice the speed of a fully double precision implementation while preserving the same level of accuracy.

Furthermore, the results indicate that decreasing the timestep improves the performance and robustness of our mixed methods, while the single precision method fails to converge.