System-free PIF Time Integrator

Single-stage or single-step high-order temporal discretizations of partial differential equations (PDEs) have shown great promise in delivering high-order accuracy in time with efficient use of computational resources. We develop the Picard Integral formulation (PIF) for finite difference method discretizations, which tightly couple spatial and temporal derivatives through the governing PDE system. 

Publication:

  1. Third-order SF-PIF3
  2. Recursive SF-PIF