HAM for Solution of the Prey and Predator Problem (original) (raw)
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Solution of the prey and predator problem by homotopy perturbation method
Applied Mathematics and Computation, 2007
In this article the problem of prey and predator is presented and the homotopy perturbation method is employed to compute an approximation to the solution of the system of nonlinear Volterra differential equations governing on the problem. The results are compared with the results using the Adomian decomposition and the power series methods. Some plots are presented to show the populations of the prey and the predator versus time for illustrating the reliability and simplicity of the method.
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Appl. Comput. …, 2011
In this study, the Volterra's prey and predator problem is investigated. Homotopy-Padé technique is utilized to find analytic solutions to the problem. Results show the accuracy of the method comparing with other methods. It is illustrated that homotopy-Padé technique can greatly enlarge the convergence region of the solution series.
A computational method for solution of the prey and predator problem
Applied Mathematics and Computation, 2005
In this article a mathematical model of the problem of prey and predator being presented and Homotopy analysis method (HAM) is employed to derive an approximation to the solution of the system of nonlinear Volterra differential equations, governing on the problem. Some examples are provided to illustrate the method. And result are also presented as plots, for the population of the prey and predator versus time.
Qualitative Analysis and Homotopy Based Solution of Two Species Lotka-Volterra Model
International journal of pure and applied mathematics, 2018
This paper presents a qualitative analysis and homotopy based solution of predator-prey Lotka-Volterra model. We established a mathematical model that shows the dynamics of a multi-species predator-prey interactions. Qualitative analysis and some qualitative information about the solution of the model have been carried out. The Homotopy Analysis Method (HAM) has been used to solve the model and the results have been compared with other numerical solution and are found to be in good agreement. Finally, various simulations are done to discuss the solution. AMS Subject Classification: 92B05, 92D25, 92D30, 93D05, 34K20, 34K25
Applied Mathematics and Computation, 2005
In this article the problem of prey and predator is presented and the power series method is employed to compute an approximation to the solution of the system of nonlinear Volterra differential equations governing the problem. The results are compared with the results using the Adomian decomposition method. Some plots are presented to show the populations of the prey and the predator versus time for illustrating the reliability and simplicity of the method.
Anali PAZU
This paper treats competitive predator-prey systems, which growth of populations and their mutual interactions are time dependent. For solving a general Lotka-Volterra system of equations, the multistage homotopy perturbation (MH-P) method is developed to predict the time evolution of the dynamical system and its properties, such as existence of stable periodic orbits. As the newest achievement, the efficiency of MH-P method is provedintreatment of almost-periodic variations of coefficients with incommensurate excitation frequencies.The periodic variations of coefficients are analyzed as special case by assuming that excitation frequencies are commensurate. By using MH-P method, the approximate analytic solutions are obtained, which are very accurate in the long term behaviour. Although an usefull convergence test of the computed solution is provided, the accuracy of MH-P method is compared also by results of the numerical integration of Lotka-Volterra equations by using the Runge...
Numerical analysis of predator-prey model in presence of toxicant by a novel approach
Journal of Mathematical and Computational Science, 2021
It is assumed in this paper that the environmental toxicant affects both prey and predator population. We consider the Holling Type-I predator-prey model and stage-structured predator-prey model in presence of environmental toxicant in the form of Volterra integro-differential equations. We solve the system of equations by a novel approach Trapezoidal Base Homotopy Perturbation Method. Using the dynamical behaviour of the systems as a validating tool, we validate the above mentioned method as an efficient method to solve Volterra integro-differential predator-prey model.
Journal of Applied Mathematics and Computing, 2011
The use of homotopy analysis method to approximate the solution of nonlinear Volterra-Fredholm integro-differential equation is proposed in this paper. In this case, the existence and uniqueness of the obtained solution and convergence of the method are proved. The accuracy of the proposed numerical scheme is examined by comparing with the modified Adomian decomposition method and Taylor polynomial method in the example. Also, the cost of operations in the algorithms are obtained to demonstrate the efficiency of the presented method. Keywords Volterra and Fredholm integral equations • Integro-differential equations • Homotopy analysis method (HAM) • Modified Adomian decomposition method (MADM) • Taylor polynomial method (TPM)
European Journal of Pure and Applied Mathematics
This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.