By applying the Adams-Bashforth-Moulton method (ABM), this paper explores complexity and synchronization of a fractional-order laser dynamical model. The dynamics under variance derivative order q parameters system have examined using multiscale algorithm bifurcation diagram. Numerical simulation outcomes demonstrate that generates chaos with decreasing q. Moreover, designs coupled network syst...

This paper introduces techniques for the estimation of solutions to fractional order differential equations (FODEs) and the approximation of a function’s Caputo fractional derivative. These techniques are based on scattered data interpolation via reproducing kernel Hilbert spaces (RKHSs). Specifically, an RKHS is generated for the purpose of estimating fractional derivatives from the Mittag-Lef...

In this paper we analyse the stability of weak discrete stationary shocks. The difference approximation is conservative, dissipative and k-th order accurate (k = 1 or k = 3). In Sections 1-3, following the previous results of D. Michelson we adapt the multistep methods RungeKutta and Adams-Bashforth to solve systems of conservation laws. In section 4 we analyse the stability of the numerical me...

Implicit-explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave, slow-wave problems in which the fast wave is physically insignificant and need not be accurately simulated. The widely used combination of trapezoidal implicit and leapfrog explicit differencing is compared to schemes based on 5 Adams methods or on backward differen...

In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM was utilized establish approximate series solutions. technique considered be an extension original Adams–Bashforth–Moulton approach. Numerical simulations and figures are discussed, in order show efficiency of proposed method. futur...

Model gerak osilasi vertikal dan torsional merupakan model yang menggambarkan pada batang digantung. Gerak naik turun suatu benda terjadi terus berulang, kemudian waktu tertentu akan berhenti atau mengalami redaman. getaran sudut dari objek rotasi. dasarnya sistem persamaan diferensial orde dua. Tujuan penelitian ini adalah untuk mengetahui solusi numerik menggunakan metode Adams-Bashforth-Moul...

we present and study the stability and convergence, and order of convergence of a numerical scheme used in geophysics, namely, the stochastic version of a deterministic “implicit leapfrog” scheme which has been developed for the approximation of the socalled barotropic vorticity model. Two other schemes which might be useful in the context of geophysical applications are also introduced and dis...