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 ...

A recently proposed numerical scheme for solving nonlinear ordinary differential equations with integer and non-integer Liouville-Caputo derivative is applied to three systems chaotic solutions. The Adams-Bashforth involving Lagrange interpolation the fundamental theorem of fractional calculus. We provide existence uniqueness solutions, also convergence result state...

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...

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed ‘Non-linear grid system’ is presented. The linear terms in Navier-Stokes equation are solved by CrankNicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Split...

A comparison between different numerical methods which are used to solve cross flow model in multicomponent membrane gas separation is studied. Considering cross flow model, numerical methods such as Bogacki-Shampine method, Dormand-Prince method, Adams-Bashforth-Moulton method, numerical differentiation formulas, modified Rosenbrock formula of order 2, Trapezoidal rule with free interpolant an...

Synchronization phenomenon has been studied intensively because of its application in many fields, and one of it is secure communication. There are many ways for synchronization, such as feedback method, adaptive techniques, time delay feedback approach, backstepping method, with nonlinear control [10]. We will prove here synchronization and anti-synchronization between two chaotic systems of d...

This paper presents a numerical model based on one-dimensional Beji and Nadaoka's Extended Boussinesq equations for simulation of periodic wave shoaling and its decomposition over morphological beaches. A unique Galerkin finite element and Adams-Bashforth-Moulton predictor-corrector methods are employed for spatial and temporal discretization, respectively. For direct application of linear fini...

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...