Coupled Nonlinear Stochastic Differential Equations

Adomian, G.

doi:10.1016/b978-0-12-044375-8.50012-5

Cited by 167 publications

(219 citation statements)

References 1 publication

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“…Among the mathematical methods employed are fourth-order Runge-Kutta [2], Maclaurin series [5], variational iteration method [6], Volterra integral form [8,9,10], Adomian decomposition method [11,12,13], and random choice method [14].…”

Section: Oxygen Diffusion In a Spherical Cell With Michaelis-menten Umentioning

confidence: 99%

Modified Taylor solution of equation of oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics

Vázquez-Leal

Sandoval-Hernandez

Castaneda-Sheissa

et al. 2015

IJAMR

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This work presents the application of a modified Taylor method to obtain a handy and easily computable approximate solution of the nonlinear differential equation to model the oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. The obtained solution is fully symbolic in terms of the coefficients of the equation, allowing to use the same solution for different values of the maximum reaction rate, the Michaelis constant, and the permeability of the cell membrane. Additionally, the numerical experiments show the high accuracy of the proposed solution, resulting 1.658509453 × 10 −15 as the lowest mean square error for a set of coefficients. The straightforward process to obtain the solution shows that the modified Taylor method is a handy alternative to a more sophisticated method because does not involve the solving of differential equations or calculate complicated integrals.

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Section: Oxygen Diffusion In a Spherical Cell With Michaelis-menten Umentioning

confidence: 99%

Modified Taylor solution of equation of oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics

Vázquez-Leal

Sandoval-Hernandez

Castaneda-Sheissa

et al. 2015

IJAMR

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“…The method was successfully applied to a large amount of applications in applied sciences. For more details about the method and its application, see ( [1][2][3][4][5][6] and [12][13]). …”

Section: Adomian Decomposition Methods (Adm)mentioning

confidence: 99%

Picard and Adomian methods for quadratic integral equation

Elsayed¹,

Hashem²,

Ziada³

2010

Comput. Appl. Math.

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“…Recently, several new techniques have been presented to overcome the mentioned difficulties. Some of these techniques include Variational Iteration Method (VIM) [9][10], decomposition method [11], Homotopy Perturbation Method (HPM) [12] [13] and Homotopy Analysis Method [14,15,16,17,18,19,20,21,22] etc. The Homotopy Analysis method (HAM) has been introduced by Liao in 1992.…”

Section: Introductionmentioning

confidence: 99%

Implementation of Homotopy Analysis Method on circular permeable slider containing of incompressible Newtonian fluid

Rahimi

Rahimi-Esbo

Ganji

et al. 2016

bspm

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The aim of this paper is to examine the classical problem of an incompressible Newtonian fluid through the porous of a circular slider which is moving laterally on a horizontal plan. Employing the similarity variables, the governing differential equations have been reduced to ordinary ones and solved via Homotopy Analysis Method (HAM). The analytical solution for the coupled Nonlinear Ordinary Differential Equations resulting from the momentum equation is obtained and Velocity fields have been computed and discussed for different values of the Reynolds number. Also the fourth-order Runge-Kutta numerical method (NUM) is used for the validity of these analytical methods and excellent agreement are observed between the solutions obtained from HAM and numerical results.

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Coupled Nonlinear Stochastic Differential Equations

Cited by 167 publications

References 1 publication

Modified Taylor solution of equation of oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics

Modified Taylor solution of equation of oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics

Picard and Adomian methods for quadratic integral equation

Implementation of Homotopy Analysis Method on circular permeable slider containing of incompressible Newtonian fluid

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