Implicit-Explicit difference schemes for nonlinear fractional differential equations with non-smooth solutions
Provides efficient numerical schemes for solving fractional differential equations with non-smooth solutions, which are common in modeling anomalous diffusion and viscoelasticity.
Proposed second-order implicit-explicit time-stepping schemes for nonlinear fractional differential equations with non-smooth solutions, achieving uniform second-order accuracy via correction terms. Numerical examples demonstrate effectiveness for nonlinear, multi-rate, and multi-term systems.
We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order $0<β<1$. From the known structure of the non-smooth solution and by introducing corresponding correction terms, we can obtain uniformly second-order accuracy from these schemes. We prove the convergence and linear stability of the proposed schemes. Numerical examples illustrate the flexibility and efficiency of the IMEX schemes and show that they are effective for nonlinear and multi-rate fractional differential systems as well as multi-term fractional differential systems with non-smooth solutions.