In this paper, we investigate the impact of network densification on the performance in terms of downlink signalto-interference (SIR) coverage probability and network area spectral efficiency (ASE). A sophisticated bounded dual-slope path loss model and practical user equipment (UE) densities are incorporated in the analysis, which have never been jointly considered before. By using stochastic ...

We consider Liénard type and frequency-damped oscillator equations. Integrating factors and the associated first integrals are derived from the method to compute λ-symmetries and the associated reduction algorithm. The knowledge of a λ-symmetry of the equation permits the determination of an integrating factor or a first integral by means of coupled first-order linear systems of partial differe...

Maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that time-dependent solution equation with appropriate initial and boundary conditions nonlinear operator preserves all time uniform pointwise absolute value. It has been challenging problem on how to design unconditionally MBP-preserving high-order accurate time-stepping sch...