Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4

homotopy analysis method Related Abstracts

4 The Solution of Nonlinear Partial Differential Equation for The Phenomenon of Instability in Homogeneous Porous Media by Homotopy Analysis Method

Authors: M. N. Mehta, Kajal K. Patel, T. R. Singh

Abstract:

When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software.

Keywords: viscosity, capillary pressure, homotopy analysis method, instability phenomenon

Procedia PDF Downloads 313
3 A Study on the Solutions of the 2-Dimensional and Forth-Order Partial Differential Equations

Authors: O. Acan, Y. Keskin

Abstract:

In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: variational iteration method, homotopy analysis method, reduced differential transform method, adomian decomposition method

Procedia PDF Downloads 282
2 Multivalued Behavior for a Two-Level System Using Homotopy Analysis Method

Authors: Angelo I. Aquino, Luis Ma. T. Bo-ot

Abstract:

We use the Homotopy Analysis Method (HAM) to solve the system of equations modeling the two-level system and extract results which will pinpoint to turbulent behavior. We look at multi-valued solutions as indicative of turbulence or turbulent-like behavior. We take di erent speci c cases which result in multi-valued velocities. The solutions are in series form and application of HAM ensures convergence in some region.

Keywords: equation, homotopy analysis method, multivalued solutions, two-level system

Procedia PDF Downloads 446
1 A Series Solution of Fuzzy Integro-Differential Equation

Authors: Mahmood Otadi, Maryam Mosleh

Abstract:

The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: homotopy analysis method, fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation

Procedia PDF Downloads 372