The energy dissipation law and the maximum bound principle (MBP) are two important physical features of well-known Allen--Cahn equation. While some commonly used first-order time stepping schemes have turned out to preserve unconditionally both MBP for equation, restrictions on step size still needed existing second-order or even higher order in such simultaneous preservation. In this paper, we...

Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, while being successful generic systems, have limited tolerance to time step size due stability accuracy constraints. We propose use data innovate classical integrators so that they can be adaptive large are tailored ea...

In this paper the throughput performance of Simple Automatic Repeat reQuest (ARQ) and Hybrid type-II ARQ schemes over Rayleigh fading channels are studied. Some new hybrid type-II schemes based on Rate Compatible Punctured Convolutional (RCPC) codes are proposed which can be regarded as a combination of simple ARQ and traditional hybrid type-II ARQ schemes. It is shown that the suggested scheme...

the category whose objects aremorphisms of fine saturated log schemes Y log → X , where Y is a noetherian scheme, and the underlying morphism of schemes Y → X is of finite type, and whose morphisms (from an object Y log 1 → X log to an object Y log 2 → X ) are morphisms of finite type Y log 1 → Y log 2 (i.e., morphisms for which the underlying morphism of schemes Y1 → Y2 is of finite type) lyin...

Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions.  The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach ...