A method to solve Convection-Diffusion equation based on homotopy analysis method

Fallahzadeh, Amir; Shakibi, K.

doi:10.5899/2015/jiasc-00074

Cited by 11 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Substituting equation (21) into equation (20), and merging the same term of q, we can obtain: We suppose that the solutions of equation (22a) are:…”

Section: Period-doubling Solutionmentioning

confidence: 99%

Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

Qiang

Qian

Guo

2019

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

A two-degree-of-freedom coupled Duffing system with time delay is studied by a modified homotopy analysis method. First, a detailed calculation is given for the system. Second, single periodic and period-doubling solutions are obtained by solving the constructed nonlinear algebraic equation. Third, upon comparison of the periodic solution obtained by the multi-frequency homotopy analysis method with the numerical solutions obtained by the numerical method, it is found that the approximate solution agrees well with the numerical solution for the system. Finally, we discuss the convergence control parameters and convergence control function.

show abstract

“…Substituting equation (21) into equation (20), and merging the same term of q, we can obtain: We suppose that the solutions of equation (22a) are:…”

Section: Period-doubling Solutionmentioning

confidence: 99%

Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

Qiang

Qian

Guo

2019

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

show abstract

“…The HAM method also provides a simple way to ensure the convergence of the series solution. Moreover, the HAM provides a large degree of freedom to choose an appropriate base function to approximate the linear and non-linear problems ( Abbasbandy, 2006;Fallahzadeh & Shakibi, 2015). Another important advantage of this method is that one can construct a continuous mapping of an initial guess approximation to the exact solution of the given problem through an auxiliary linear operator.…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical method applied to turbocharger engine model

Nave

2020

JART

View full text Add to dashboard Cite

In this study, we apply a new version of the Homotopy Analysis Method called decomposition of the homotopy analysis method (DHAM). The DHAM method is based on the decomposition of the right-hand side of a given system of differential equations into a sum of functions. After the decomposition one can apply the HAM method. The physical model that we investigate in this paper is a complex system of equations that contains nonlinear ordinary differential equations of the first order. The system of equations takes into account the important variables such as the pressure, the temperature, the mass flow, the torque due to the turbine turbocharger, the torque from the compressor, the speed of turbocharger, etc. This system is very complex and cannot be solved analytically. The HAM method includes an artificial small parameter that inserts into the physical model and hence it enables one to apply different asymptotic methods. We compared the results of DHAM and HAM to numerical simulations analyses. We concluded that the DHAM results are closer to the numerical simulation results.

show abstract

“…This equation is a parabolic differential equation which describes physical phenomena. In their work they considered the following linear convection diffusion (CD) equation and the homotopy analysis method was applied to solve it, [4].…”

Section: Introductionmentioning

confidence: 99%

Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Chioma¹,

Ugonna²,

Michael³

et al. 2019

MMA

View full text Add to dashboard Cite

In this paper, we modified the model of [23] and then applied a new semi-analytic technique namely the Homotopy Analysis Method (HAM) in solving the SEIRS Epidemic Mathematical Model. The modified SEIRS model wasfirst formulated and adequately analyzed. We investigated the basic properties of the model by proving the positivity of the solutions and establishing the invariant region. We further obtained the steady states: disease-free equilibrium (DFE) and endemic equilibrium (EE), then we went further to determine the local stability of the DEF and EE using the basic reproduction number which was calculated. We also applied Lyaponuv method to prove the global stability of endemic equilibrium, The HAM was applied to obtain an accurate solution to the model in few iterations. Finally, a numerical solution (simulation) of the model was obtained using MAPLE 15 computation software.

show abstract

A method to solve Convection-Diffusion equation based on homotopy analysis method

Cited by 11 publications

References 12 publications

Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

A semi-analytical method applied to turbocharger engine model

Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Contact Info

Product

Resources

About