Abstract:Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu's equation, Troesch's problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. … Show more
“…Most models of real life problems are still very difficult to solve. Therefore, approximate analytical solutions such as Homotopy perturbation method (HPM) [10][11][12][13][14][15][16][17][18][19][20][21][22][23] were introduced. This method is the most effective and convenient ones for both linear and non-linear equations.…”
Section: Analytical Expression Of Concentration Of Oxygen Using New Hmentioning
confidence: 99%
“…The HPM is unique in its applicability, accuracy and efficiency. The HPM [18][19][20][21][22][23] uses the imbedding parameter p as a small parameter, and only a few iterations are needed to search for an asymptotic solution. The law of mass action of oxygen uptake leads to the following non-linear equations…”
Section: Analytical Expression Of Concentration Of Oxygen Using New Hmentioning
This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.
“…Most models of real life problems are still very difficult to solve. Therefore, approximate analytical solutions such as Homotopy perturbation method (HPM) [10][11][12][13][14][15][16][17][18][19][20][21][22][23] were introduced. This method is the most effective and convenient ones for both linear and non-linear equations.…”
Section: Analytical Expression Of Concentration Of Oxygen Using New Hmentioning
confidence: 99%
“…The HPM is unique in its applicability, accuracy and efficiency. The HPM [18][19][20][21][22][23] uses the imbedding parameter p as a small parameter, and only a few iterations are needed to search for an asymptotic solution. The law of mass action of oxygen uptake leads to the following non-linear equations…”
Section: Analytical Expression Of Concentration Of Oxygen Using New Hmentioning
This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.
The mathematical modeling of nonlinear boundary value problems in catalytically chemical reactor is discussed. In this paper, we obtain the approximate analytical solution and the effectiveness factors for the evolution of single-step transformations under non-isothermal conditions using homotopy perturbation method. We have applied it to many reaction models and obtained very simple analytical expressions for the shape of the corresponding transformation rate peaks. These analytical solutions represent a significant simplification of the system’s description allowing easy curve fitting to experiment. The accuracy achieved with our method is checked against several reaction models and numerical results. A satisfactory agreement is noted.
“…Ji Huan He used the HPM to solve the light hill equation [20], the Duffing equation [21] and the Blasius equation [22]. The idea has been used to solve non-linear boundary value problems, integral equations and many other problems [23][24][25][26][27]. The HPM is unique in its applicability, accuracy and efficiency.…”
Section: Analytical Expressions Of Concentrations Using Homotopy Pertmentioning
A mathematical model of the oscillatory regimes of CO oxidation over plantinum-group metal catalysts are discussed. The model is based on nonstationary diffusion equation containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents the analytical and numerical solution of the system of non-linear differential equations. Here the Homotopy perturbation method (HPM) is used to find out the analytical expressions of the concentration of CO molecules, O atom and oxide oxygen respectively. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical and numerical results is observed.
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