74 research outputs found
Solving One-Predator Two-Prey System by using Adomian Decomposition Method / Wan Khairiyah Hulaini Wan Ramli... [et. al]
In this paper, a mathematical model of one-predator two-prey system is discussed. This model is derived from predator-prey Lotka-Volterra model by adding another population of prey into the system. The model derived is a nonlinear system of ODEs. So the approach to this model is different from the linear system of ODEs. With reference to that, Adomian Decomposition Method (ADM) is one of the semi-analytical approaches being applied in this paper to solve the system. The approximate solution is made until four terms. The solution obtained is analyzed graphically
A fractional B-spline collocation method for the numerical solution of fractional predator-prey models
We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approximating space. Then, in the collocation step the fractional derivative of the approximating function is approximated accurately and efficiently by an exact differentiation rule that involves the generalized finite difference operator. To show the effectiveness of the method for the solution of nonlinear dynamical systems of fractional order, we solved the fractional Lotka-Volterra model and a fractional predator-pray model with variable coefficients. The numerical tests show that the method we proposed is accurate while keeping a low computational cost
Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach
In this article we provide homotopy solutions of a cancer nonlinear model
describing the dynamics of tumor cells in interaction with healthy and effector
immune cells. We apply a semi-analytic technique for solving strongly nonlinear
systems - the Step Homotopy Analysis Method (SHAM). This algorithm, based on a
modification of the standard homotopy analysis method (HAM), allows to obtain a
one-parameter family of explicit series solutions. By using the homotopy
solutions, we first investigate the dynamical effect of the activation of the
effector immune cells in the deterministic dynamics, showing that an increased
activation makes the system to enter into chaotic dynamics via a
period-doubling bifurcation scenario. Then, by adding demographic stochasticity
into the homotopy solutions, we show, as a difference from the deterministic
dynamics, that an increased activation of the immune cells facilitates cancer
clearance involving tumor cells extinction and healthy cells persistence. Our
results highlight the importance of therapies activating the effector immune
cells at early stages of cancer progression
Some Problems on Variational Iteration Method
In this research project paper, I introduce some basic idea of Variational iteration method and its algorithm to solve the equations ODE & PDE, fractional differential equation, fractal differential equation and differential-difference equations. Also, some linear and nonlinear differential equations like Burger’s equation, Fisher’s equation,Wave equation and Schrodinger equation are solved by using Variational iteration method. Then I compare this method with Adomian decomposition method (ADM) and modified Variational iteration method (MVIM). The advantage of VIM, it does not require a small parameter in an equation as perturbation technique needs. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, its exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified
Nonsensical models for quantum dots
We analyze a model proposed recently for the calculation of the energy of an
exciton in a quantum dot and show that the authors made a serious mistake in
the solution to the Schr\"{o}dinger equation
A hybrid functions method for solving linear and non-linear systems of ordinary differential equations
In the present paper, we use a hybrid method to solve linear or non-linear systems of ordinary differential equations (ODEs). By using this method, these systems are reduced to a linear or non-linear system of algebraic equations. In error discussion of the suggested method, an upper bound of the error is obtained. Also, to survey the accuracy and the efficiency of the present method, some examples are solved and comparisons between the obtained results with those of several other methods are carried out
Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting Using Homotopy Perturbation Method
Due to wide range of interest in use of bioeconomic models to gain insight into the
scientific management of renewable resources like fisheries and forestry, homotopy perturbation
method is employed to approximate the solution of the ratio-dependent predator-prey system with
constant effort prey harvesting. The results are compared with the results obtained by Adomian
decomposition method. The results show that, in new model, there are less computations needed
in comparison to Adomian decomposition method
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