Solution of Simple Prey-Predator Model by Runge Kutta Method

Juarlin, Eko

doi:10.1088/1742-6596/1341/6/062024

Cited by 3 publications

(1 citation statement)

References 1 publication

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“…The Runge-Kutta method as a numerical method is used for comparative analysis to obtaining numerical approximation for the system of nonlinear differential equation [14] such as predator-prey model and applicable to economical models [26]. In this paper, the built-in function of the fourth order classical Runge-Kutta method is considered to obtain an approximate solution for an initial value problem (IVP) [27], to implement this method of solution, x(t) and y(t) represent the predator-prey population of the IVP over the time interval…”

Section: Classical Runge-kutta Methodsmentioning

confidence: 99%

An Approximate Solution to Predator-prey Models Using The Differential Transform Method and Multi-step Differential Transform Method, in Comparison with Results of The Classical Runge-kutta Method

Adeniji¹,

A²,

Mkolesia³

et al. 2021

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Predator-prey models are the building blocks of the ecosystems as biomasses are grown out of their resource masses. Different relationships exist between these models as different interacting species compete, metamorphosis occurs and migrate strategically aiming for resources to sustain their struggle to exist. To numerically investigate these assumptions, ordinary differential equations are formulated, and a variety of methods are used to obtain and compare approximate solutions against exact solutions, although most numerical methods often require heavy computations that are time-consuming. In this paper, the traditional differential transform (DTM) method is implemented to obtain a nu-merical approximate solution to prey-predator models. The solution obtained with DTM is convergent locally within a small domain. The multi-step differential transform method (MSDTM) is a technique that improves DTM in the sense that it increases its interval of convergence of the series expansion.One predator-one prey and two-predator-one prey models are considered with a quadratic term which signifies other food sources for its feeding. The result obtained numerically and graphically showspoint DTM diverges. The advantage of the new algorithm is that the obtained series solution converges for wide time regions and the solutions obtained from DTM and MSDTM are compared with so-lutions obtained using the classical Runge-Kutta method of order four. The results demonstrated is that MSDTM computes fast, is reliable and gives good results compared to the solutions obtained using the classical Runge-Kutta method.

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Section: Classical Runge-kutta Methodsmentioning

confidence: 99%

An Approximate Solution to Predator-prey Models Using The Differential Transform Method and Multi-step Differential Transform Method, in Comparison with Results of The Classical Runge-kutta Method

Adeniji¹,

A²,

Mkolesia³

et al. 2021

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Noise-induced control of environmental fluctuations in a three-species predator–prey model

Das

Srinivash

Kabir

et al. 2020

Model. Earth Syst. Environ.

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Research on cold chain logistics optimization model considering low-carbon emissions

Ning

Han

Fang

2023

International Journal of Low-Carbon Technologies

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Cold chain logistics distribution orders have increased due to the impact of COVID-19. In view of the increasing difficulty of route optimization and the increase of carbon emissions in the process of cold chain logistics distribution, a mathematical model for route optimization of cold chain logistics distribution vehicles with minimum comprehensive cost is established by considering the cost of carbon emission intensity comprehensively in this paper. The main contributions of this paper are as follows:1.An improved hybrid ant colony algorithm is proposed, which combined simulated annealing algorithm to get rid of the local optimal solution.2. Chaotic mapping is introduced in pheromone update to accelerate convergence and improve search efficiency. The effectiveness of the proposed method in optimizing cold chain logistics distribution path and reducing costs is verified by simulation experiments and comparison with the existing classical algorithms.

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Solution of Simple Prey-Predator Model by Runge Kutta Method

Cited by 3 publications

References 1 publication

An Approximate Solution to Predator-prey Models Using The Differential Transform Method and Multi-step Differential Transform Method, in Comparison with Results of The Classical Runge-kutta Method

An Approximate Solution to Predator-prey Models Using The Differential Transform Method and Multi-step Differential Transform Method, in Comparison with Results of The Classical Runge-kutta Method

Noise-induced control of environmental fluctuations in a three-species predator–prey model

Research on cold chain logistics optimization model considering low-carbon emissions

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