Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey–predator problem

Lu, Yu; Li, Meng

doi:10.1007/s40314-023-02261-6

Cited by 4 publications

(1 citation statement)

References 61 publications

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“…Prey-Predator has been implemented in several research studies [39][40][41]. The best prey is dedicated to thoroughly exploiting its immediate vicinity, while the predator's task is to traverse the search space in pursuit of promising regions.…”

Section: Related Workmentioning

confidence: 99%

A Discrete Prey–Predator Algorithm for Cloud Task Scheduling

Abdulgader,

Yousif,

Ali

2023

Applied Sciences

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Cloud computing is considered a key Internet technology. Cloud providers offer services through the Internet, such as infrastructure, platforms, and software. The scheduling process of cloud providers’ tasks concerns allocating clients’ tasks to providers’ resources. Several mechanisms have been developed for task scheduling in cloud computing. Still, these mechanisms need to be optimized for execution time and makespan. This paper presents a new task-scheduling mechanism based on Discrete Prey–Predator to optimize the task-scheduling process in the cloud environment. The proposed Discrete Prey–Predator mechanism assigns each scheduling solution survival values. The proposed mechanism denotes the prey’s maximum surviving value and the predator’s minimum surviving value. The proposed Discrete Prey–Predator mechanism aims to minimize the execution time of tasks in cloud computing. This paper makes a significant contribution to the field of cloud task scheduling by introducing a new mechanism based on the Discrete Prey–Predator algorithm. The Discrete Prey–Predator mechanism presents distinct advantages, including optimized task execution, as the mechanism is purpose-built to optimize task execution times in cloud computing, improving overall system efficiency and resource utilization. Moreover, the proposed mechanism introduces a survival-value-based approach, as the mechanism introduces a unique approach for assigning survival values to scheduling solutions, differentiating between the prey’s maximum surviving value and the predator’s minimum surviving value. This improvement enhances decision-making precision in task allocation. To evaluate the proposed mechanism, simulations using the CloudSim simulator were conducted. The experiment phase considered different scenarios for testing the proposed mechanism in different states. The simulation results revealed that the proposed Discrete Prey–Predator mechanism has shorter execution times than the firefly algorithm. The average of the five execution times of the Discrete Prey–Predator mechanism was 270.97 s, while the average of the five execution times of the firefly algorithm was 315.10 s.

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Section: Related Workmentioning

confidence: 99%

A Discrete Prey–Predator Algorithm for Cloud Task Scheduling

Abdulgader,

Yousif,

Ali

2023

Applied Sciences

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Finite element analysis of time‐fractional integro‐differential equation of Kirchhoff type for non‐homogeneous materials

Kumar,

Sista,

Sreenadh

2023

Math Methods in App Sciences

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In this paper, we study a time‐fractional initial‐boundary value problem of Kirchhoff type involving memory term for non‐homogeneous materials. As a consequence of energy argument, we derive bound as well as bound on the solution of the considered problem by defining two new discrete Laplacian operators. Using these a priori bounds, existence and uniqueness of the weak solution to the considered problem are established. Further, we study semi discrete formulation of the problem by discretizing the space domain using a conforming finite element method (FEM) and keeping the time variable continuous. The semi discrete error analysis is carried out by modifying the standard Ritz‐Volterra projection operator in such a way that it reduces the complexities arising from the Kirchhoff type nonlinearity. Finally, we develop a new linearized L1 Galerkin FEM to obtain numerical solution of the problem under consideration. This method has a convergence rate of , where is the fractional derivative exponent and and are the discretization parameters in the space and time directions, respectively. This convergence rate is further improved to second order in the time direction by proposing a novel linearized L2‐1 Galerkin FEM. We conduct a numerical experiment to validate our theoretical claims.

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Unconditional superconvergence analysis of an energy-stable L1 scheme for coupled nonlinear time-fractional prey-predator equations with nonconforming finite element

Shi,

Zhang

2024

Applied Mathematics and Computation

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Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey–predator problem

Cited by 4 publications

References 61 publications

A Discrete Prey–Predator Algorithm for Cloud Task Scheduling

A Discrete Prey–Predator Algorithm for Cloud Task Scheduling

Finite element analysis of time‐fractional integro‐differential equation of Kirchhoff type for non‐homogeneous materials

Unconditional superconvergence analysis of an energy-stable L1 scheme for coupled nonlinear time-fractional prey-predator equations with nonconforming finite element

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