Chaobao Huang

Unconditional Optimal Error Estimates of a Linearized Nonuniform Alikhanov Scheme for Nonlinear Superdiffusion Equations

In this paper, we consider a nonlinear fractional superdiffusion equation involving a Caputo derivative of order α∈(1,2). Solutions to this class of problems typically exhibit weak singularities near the initial time. To handle this singularity, we introduce an auxiliary variable p:=Dtα/2(u−tu1) and reformulate the ori...