The solution of initial value problems of large systems of ordinary differential equations (ODEs) is computationally intensive and demands for efficient parallel solution techniques that take into account the complex architectures of modern parallel computer systems. This article discusses implementation techniques suitable for ODE systems with a special coupling structure, called limited acces...

Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps precisely where the smallest elements in the mesh are located. Starting from classical Adams-Bashforth multi-step methods, local time-stepping methods of arbitr...

This paper presents the comparison of two Adams methods using extrapolation for best method suitable approximation solutions. The (Adams Moulton and Bashforth) step k = 3 to 4 are considered their equations derived. points, order, error constant, stability regions were also derived steps. More importantly, consistency zero investigated finally, used solve some non-stiff differential in efficien...

In this article, we conjugate time marching schemes with Finite Differences splittings into low and high modes in order to build fully explicit methods with enhanced temporal stability for the numerical solutions of PDEs. The main idea is to apply explicit schemes with less restrictive stability conditions to the linear term of the high modes equation, in order that the allowed time step for th...

We present a derivation and theoretical investigation of the Adams-Bashforth and Adams-Moulton family of linear multistep methods for solving ordinary differential equations, starting from a Gaussian process (GP) framework. In the limit, this formulation coincides with the classical deterministic methods, which have been used as higher-order initial value problem solvers for over a century. Fur...

Regenerative chatter is the most important factor affecting stability of milling process. It core for suppressing and improving production efficiency to accurately efficiently identify stable region chatter. Therefore, according theory predictor-corrector, three predictor–corrector methods (PCM) are, respectively, proposed by applying fourth-order Adams-Bashforth-Moulton formula, Simpson Hammin...

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 propose and study two second-order in time implicit-explicit (IMEX) methods for the coupled Stokes-Darcy system that governs flows in karst aquifers. The first is a combination of a second-order backward differentiation formula and the second-order Gear’s extrapolation approach. The second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algor...