New Numerical Scheme with Newton Polynomial

In this paper, we present a new numerical scheme for a model involving new mathematical concepts that are of great importance for interpreting and examining real world problems. Firstly, we handle a Labyrinth chaotic problem with fractional operators which include exponential decay, power-law and Mittag-Leffler kernel. Moreover, this problem is solved via Atangana-Seda numerical scheme which is based on Newton polynomial. The accuracy and efficiency of the method can be easily seen with numerical simulations.

Download Full-text

NUMERICAL SCHEME OF THE WAHA CODE

Multiphase Science and Technology ◽

10.1615/multscientechn.v20.i3-4.50 ◽

2008 ◽

Vol 20 (3-4) ◽

pp. 323-354 ◽

Cited By ~ 8

Author(s):

Iztok Tiselj ◽

A. Horvat ◽

J. Gale

Keyword(s):

Numerical Scheme

Download Full-text

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

NONEQUILIBRIUM PROCESSES: RECENT ACCOMPLISHMENTS ◽

10.30826/nepcap9a-47 ◽

2020 ◽

Author(s):

A. I. Lopato ◽

◽

A. G. Eremenko ◽

Keyword(s):

Chemical Kinetics ◽

Numerical Scheme ◽

Unstructured Grids ◽

Numerical Study ◽

Numerical Approach ◽

Detonation Waves ◽

Detailed Chemical Kinetics ◽

Parallel Solver ◽

Further Development ◽

Detailed Chemical

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.

Download Full-text

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

Revista Mexicana de Física ◽

10.31349/revmexfis.67.91 ◽

2021 ◽

Vol 67 (1 Jan-Feb) ◽

pp. 91

Author(s):

N. Sene

Keyword(s):

Caputo Derivative ◽

Local Stability ◽

Numerical Scheme ◽

Equilibrium Points ◽

Electrical Circuit ◽

Maximal Lyapunov Exponent ◽

Electrical Circuits ◽

Adaptive Controls ◽

Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

Download Full-text