The numerical simulation for stiff systems of ordinary differential equations

Darvishi, M. T.; Khani, F.; Soliman, Ahmed

doi:10.1016/j.camwa.2006.12.072

Cited by 58 publications

(30 citation statements)

References 24 publications

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“…Therefore, there have been attempts to develop new techniques for obtaining analytical solutions which reasonably approximate the exact solutions [1]. In recent years, several such techniques have drawn special attention, such as Hirota's bilinear method [2], the homogeneous balance method [3,4], inverse scattering method [5], Adomian's decomposition method ADM [6,7], the variational iteration method [8,9] and the δ-expansion method [10] as well as homotopy analysis method (HAM). Firstly, Liao in 1992 employed the basic idea of homotopy in topology to propose a general analytic method for nonlinear problems [11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A series solution of the foam drainage equation

Darvishi

Khani²

2009

Computers & Mathematics with Applications

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a b s t r a c tFoaming occurs in many distillation and absorption processes. The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. In this paper, we apply an analytic technique, namely the homotopy analysis method (HAM) to handle the foam drainage equation. The powerful homotopy analysis method computes the solution in a rapidly convergent infinite series. We also compare the numerical results obtained by HPM or ADM and the same results obtained by using the analytic solutions obtained by HAM.

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Section: Introductionmentioning

confidence: 99%

A series solution of the foam drainage equation

Darvishi

Khani²

2009

Computers & Mathematics with Applications

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“…Darvishi et al [23] solved this system by the variational iteration method. According to HPM, we can construct a homotopy of system (7) as…”

Section: Problemmentioning

confidence: 99%

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

Darvishi

Khani²

2008

Zeitschrift Für Naturforschung A

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“…Consider the dimensionless nonlinear boundary value problem describing temperature distribution in a uniformly thick rectangular fin with radiation to free space [10] …”

Section: Example Problemmentioning

confidence: 99%

Review of the New Perturbation-Iteration Method

Pakdemi̇rli̇

2013

MCA

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Abstract-The new perturbation iteration method developed by Pakdemirli and coworkers are reviewed. First, applications of the method to algebraic equations are discussed and some new root-finding algorithms developed by this method are given. Next, the applications of the new method to first order, second order and systems of first order ordinary differential equations are discussed. Three sample problems are selected. Results are compared with analytical solutions, solutions by other methods and numerical solutions. The new perturbation iteration method is an effective method that does not require small parameter assumption as in classical perturbation methods.

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The numerical simulation for stiff systems of ordinary differential equations

Cited by 58 publications

References 24 publications

A series solution of the foam drainage equation

A series solution of the foam drainage equation

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

Review of the New Perturbation-Iteration Method

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