A linearized spectral Galerkin/finite difference approach is developed for variable fractional-order nonlinear diffusion–reaction equations with a fixed time delay. The temporal discretization the variable-order fractional derivative performed by L1-approximation. An appropriate basis function in terms of Legendre polynomials used to construct Galerkin method spatial second-order operator. main...

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for...

This paper addresses an approximation-based anti-windup (AW) control strategy for suppressing the windup effect caused by actuator saturation nonlinearity in proportional–integral–derivative (PID) controlled systems. The effect of actuator constraint is firstly regarded as a disturbance imported to the PID controller. The external disturbance can then be modeled by a linear differential equatio...

The Cannings exchangeable model for a finite population in discrete time is extended to incorporate selection. The probability of fixation of a mutant type is studied under the assumption of weak selection. An exact formula for the derivative of this probability with respect to the intensity of selection is deduced, and developed in the case of a single mutant. This formula is expressed in term...