Section: New Results

An exponential Adams–Bashforth ODE solver for stiff problems

C. Douanla Lontsi, together with Y. Coudière and C. Pierre, obtained an important result on time integration of stiff differential problems. They considered Adams exponential integrators with general varying stabilizers. General stabilization brings flexibility and facilitates the integration of ODE systems and semilinear evolution PDEs coupled with ODE systems. They were able to prove the stability and convergence of this type of integrator by introducing a new framework that extends multistep linear methods. Dahlquist stability was numerically investigated. A(α)-stability was observed under a condition on the stabilizer, which is a singular property for explicit schemes. The method was numerically studied for two stiff models in electrophysiology. Its performance was compared with several classical methods. The authors concluded that for stiff ODE systems, it provides a cheaper way to compute accurate solutions at large time steps than implicit solvers.