This paper concerns the dissipativity and stability of the Caputo nonlinear fractional functional differential equations (F-FDEs) with order 0 < α < 1. The fractional generalization of the Halanay-type inequality is proposed, which plays a central role in studies of stability and dissipativity of F-FDEs. Then the dissipativity and the absorbing set are derived under almost the same assumptions ...

We develop the third-order adaptive Adams-Bashforth time integration and second-order finite difference equation for variable steps. incorporate these schemes in Celeris Advent software to discretize solve 2D extended Boussinesq equations. This uses a hybrid volume – scheme leverages GPU equations faster than real-time while concurrently visualizing them. The newly added significantly improves ...

Visceral leishmaniosis is one recent example of a global illness that demands our best efforts at understanding. Thus, mathematical modeling may be utilized to learn more about and make better epidemic forecasts. By taking into account the Caputo Caputo-Fabrizio derivatives, frictional model visceral was mathematically examined based on real data from Gedaref State, Sudan. The stability analysi...

We introduce new projective versions of second-order accurate Runge-Kutta and Adams-Bashforth methods, and demonstrate their use as outer integrators in solving stiff differential systems. An important outcome is that the new outer integrators, when combined with an inner telescopic projective integrator, can result in fully explicit methods with adaptive outer step size selection and solution ...

Semi-implicit multistep methods are an efficient tool for solving large-scale ODE systems. This recently emerged technique is based on modified Adams–Bashforth–Moulton (ABM) methods. In this paper, we introduce new semi-explicit and semi-implicit predictor–corrector the backward differentiation formula Adams–Bashforth We provide a thorough study of numerical stability performance compare their ...

Transient stability-constrained optimal power flow (TSCOPF) models comprehensively analyze the security and economic operation of systems. However, they require a high computational effort can suffer from convergence problems when applied to large This study analyzes performance eleven numerical integration algorithms ordinary differential equations that represent system dynamics in TSCOPF mode...

Surface tension is a meaningful parameter influencing boiling and condensation in macroscopic scale, confined spaces, or for nanofluids; it further affects with surfactants. Surface, interfacial, an important property the research into increasing heat transfer, enhancing efficiency of photovoltaic systems, improving engine operation, forming drugs polymers. It often determined using axisymmetri...

In this paper the Benettin-Wolf algorithm to determine all Lyapunov exponents adapted a class of non-commensurate fractional-order systems modeled by Caputo's derivative and corresponding Matlab code are presented. The continues work started in [Danca & Kuznetsov, 2018], where commensurate is given. To integrate extended system, Adams-Bashforth-Moulton for fractional differential equations util...

We outline a new class of robust and efficient methods for solving the Navier– Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams–Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experime...

We consider variations of the Adams–Bashforth, backward differentiation, and Runge–Kutta families of time integrators to solve systems of linear wave equations on uniform, time-staggered grids. These methods are found to have smaller local truncation errors and to allow larger stable time steps than traditional nonstaggered versions of equivalent orders. We investigate the accuracy and stabilit...