Solution of a nonlinear time-delay model in biology via semi-analytical approaches

Dehghan, Mehdi; Salehi, Rezvan

doi:10.1016/j.cpc.2010.03.014

Cited by 91 publications

(49 citation statements)

References 70 publications

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“…Many different methods have been developed for tackling NEEs from both analytical and numerical point of views. Some recent ones include: homogeneous balance method [1], tanh function method [2], (G'/G)-expansion method [3], Exp-function method [4], F-expansion method [5], homotopy perturbation method [6][7][8][9][10], the solitary wave ansatz method [11], multiple Exp-function method [12], Adomian-Pade technique [13], further improved F-expansion method [14], and variational iteration method [15][16][17][18], etc. However, different methods are required for different targets because each mathematical method has its own features.…”

Section: Introductionmentioning

confidence: 99%

The first integral method for constructing exact and explicit solutions to nonlinear evolution equations

Aslan

2012

Math Methods in App Sciences

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Communicated by S. GeorgievProblems that are modeled by nonlinear evolution equations occur in many areas of applied sciences. In the present study, we deal with the negative order KdV equation and the generalized Zakharov system and derive some further results using the so-called first integral method. By means of the established first integrals, some exact traveling wave solutions are obtained in a concise manner.

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Section: Introductionmentioning

confidence: 99%

The first integral method for constructing exact and explicit solutions to nonlinear evolution equations

Aslan

2012

Math Methods in App Sciences

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“…Consider the linear non-homogeneous fractional KdV equation [9] as follows: (70) where b and c are constants, 0 < α ≤ 1, and g(x,t), the source term, is a function of x and t. We assume that the initial and boundary conditions are…”

Section: T) (24)mentioning

confidence: 99%

Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

Dehghan

Manafian

Saadatmandi

2010

Zeitschrift Für Naturforschung A

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In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

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“…Dehghan and Salehi [21] used VIM and ADM to solve the delay logistic equation which has been extensively used as models in biology with particular emphasis on population dynamics. In 2009, Li [8] applied VIM to solve the model (B) with great success, but ADM, HPM and HAM have yet not been used for the purpose.…”

Section: 0t Umentioning

confidence: 99%

Analytic algorithms for Some Models of Nonlinear Age–Structured Population Dynamics and Epidemiology

Baranwal¹,

Pandey²,

Tripathi³

et al. 2011

JMP

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Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and accuracy of the methods.

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Solution of a nonlinear time-delay model in biology via semi-analytical approaches

Cited by 91 publications

References 70 publications

The first integral method for constructing exact and explicit solutions to nonlinear evolution equations

The first integral method for constructing exact and explicit solutions to nonlinear evolution equations

Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

Analytic algorithms for Some Models of Nonlinear Age–Structured Population Dynamics and Epidemiology

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