scholarly journals Numerical study for fractional model of non-linear predator-prey biological population dynamical system

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2017-2025 ◽  
Author(s):  
Jagdev Singh ◽  
Adem Kilicman ◽  
Devendra Kumar ◽  
Ram Swroop ◽  
Fadzilah Ali
Keyword(s):  
Dynamical System ◽  
Population Model ◽  
Numerical Scheme ◽  
Series Solution ◽  
Numerical Study ◽  
Computational Approach ◽  
Predator Prey ◽  
Biological Population ◽  
Non Linear ◽  
Homotopy Analysis

The key objective of the present paper is to propose a numerical scheme based on the homotopy analysis transform technique to analyze a time-fractional non-linear predator-prey population model. The population model are coupled fractional order non-linear PDE often employed to narrate the dynamics of biological systems in which two species interact, first is a predator and the second is a prey. The proposed scheme provides the series solution with a great freedom and flexibility by choosing appropriate parameters. The convergence of the results is free from small or large parameters. Three examples are discussed to demonstrate the correctness and efficiency of the used computational approach.

scholarly journals Numerical study for fractional model of nonlinear predator-prey biological population dynamic system

2018 ◽  
Author(s):  
Jagdev Singh ◽  
Adem Kilicman ◽  
Devendra Kumar ◽  
Ram Swroop
Keyword(s):  
Population Dynamic ◽  
Population Model ◽  
Numerical Scheme ◽  
Series Solution ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Computational Approach ◽  
Predator Prey ◽  
Biological Population ◽  
Homotopy Analysis

The key objective of the present paper is to propose a numerical scheme based on the homotopy analysis transform technique to analyze the time-fractional nonlinear predator-prey population model. The population model is coupled fractional order nonlinear partial differential equations often employed to narrate the dynamics of biological systems in which two species interact, first is a predator and the second is a prey. The proposed scheme provides the series solution with great freedom and flexibility by choosing appropriate parameters. The convergence of results is free from small or large parameters. Three examples are discussed to demonstrate the correctness and efficiency of the used computational approach.

scholarly journals Two Species Commensalism Model with Harvesting by Homotopy Analysis Method

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3584-3588
Keyword(s):  
Linear System ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analytical Study ◽  
Analysis Method ◽  
Linear Ordinary Differential Equations ◽  
Commensal Species ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Non Linear System

In the present investigation a two species commensalism model was taken up for detailed analytical study in which commensal species was harvested at a rate proportional to its strength. The system under investigation was represented by a coupled non linear ordinary differential equations. The series solution of the non-linear system was approximated by Homotopy Analysis Method.

An efficient computational approach for a fractional-order biological population model with carrying capacity

2020 ◽  
Vol 138 ◽  
pp. 109880 ◽  
Author(s):  
H.M. Srivastava ◽  
V.P. Dubey ◽  
R. Kumar ◽  
J. Singh ◽  
D. Kumar ◽  
...  
Keyword(s):  
Fractional Order ◽  
Carrying Capacity ◽  
Population Model ◽  
Computational Approach ◽  
Biological Population

scholarly journals Non-Differentiable Solution of Nonlinear Biological Population Model on Cantor Sets

2020 ◽  
Vol 4 (1) ◽  
pp. 5
Author(s):  
Djelloul Ziane ◽  
Mountassir Hamdi Cherif ◽  
Dumitru Baleanu ◽  
Kacem Belghaba
Keyword(s):  
Partial Differential Equations ◽  
Homotopy Analysis Method ◽  
Population Model ◽  
Nonlinear Partial Differential Equations ◽  
Cantor Sets ◽  
Analysis Method ◽  
Differentiable Solution ◽  
Derivative Operator ◽  
Biological Population ◽  
Homotopy Analysis

The main objective of this study is to apply the local fractional homotopy analysis method (LFHAM) to obtain the non-differentiable solution of two nonlinear partial differential equations of the biological population model on Cantor sets. The derivative operator are taken in the local fractional sense. Two examples have been presented showing the effectiveness of this method in solving this model on Cantor sets.

Steady free convection in a porous medium heated from below

1967 ◽  
Vol 27 (1) ◽  
pp. 29-48 ◽  
Author(s):  
J. W. Elder
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Numerical Scheme ◽  
Numerical Study ◽  
Critical Rayleigh Number ◽  
Linear Process ◽  
Wave Number ◽  
End Effects ◽  
Non Linear

This is an experimental and numerical study of steady free convection in a porous medium, a system dominated by a single non-linear process, the advection of heat. The paper presents results on three topics: (1) a system uniformly heated from below, for which the flow is cellular, as in the analogous Bénard-Rayleigh flows, (ii) the role of end-effects, and (iii) the role of mass discharge. Measurements of heat transfer are used to establish further the validity of the numerical scheme proposed by the author (1966a), while the other flows allow a more extensive study of the numerical scheme under various boundary conditions. The results are very satisfactory even though only moderately non-linear problems can be treated at present.The main new results are as follows. For the Rayleigh-type flow, above a critical Rayleigh number of about 40, the heat transferred across the layer is proportional to the square of the temperature difference across the layer and is independent of the thermal conductivity of the medium or the depth of the layer. This result is modified when the boundary-layer thickness is comparable to the grain size of the medium. The investigation of end-effects reveals variations in horizontal wave-number and a pronounced hysteresis and suggests an alternative explanation of some observations by Malkus (1954).

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

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.

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