A New Reliable Approach for Two-Dimensional and Axisymmetric Unsteady Flows Between Parallel Plates

2013 ◽  
Vol 68 (10-11) ◽  
pp. 629-634 ◽  
Author(s):  
◽  
Jagdev Singh ◽  
Yadvendra S. Shishodia
Keyword(s):  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Unsteady Flows ◽  
Solution Procedure ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Homotopy Perturbation ◽  
Roundoff Errors ◽  
Sumudu Transform

The main aim of this work is to present a new reliable approach to compute an approximate solution of the system of nonlinear differential equations governing the problem of two-dimensional and axisymmetric unsteady flows due to normally expanding or contracting parallel plates by the homotopy perturbation method, and the Sumudu transform is adopted in the solution procedure. The method finds the solution without any discretization or restrictive assumptions and avoids the roundoff errors. The numerical solutions obtained by the proposed technique indicate that the approach is easy to implement and computationally very attractive.

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

scholarly journals Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
A. Kılıçman
Keyword(s):  
Perturbation Method ◽  
Gas Dynamics ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Gas Dynamics Equation

A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.

scholarly journals Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
Adem Kılıçman
Keyword(s):  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Spatial Diffusion ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Breeding Territory ◽  
Sumudu Transform ◽  
User Friendly

The main aim of this work is to present a user friendly numerical algorithm based on homotopy perturbation Sumudu transform method for nonlinear fractional partial differential arising in spatial diffusion of biological populations in animals. The movements are made generally either by mature animals driven out by invaders or by young animals just reaching maturity moving out of their parental territory to establish breeding territory of their own. The homotopy perturbation Sumudu transform method is a combined form of the Sumudu transform method and homotopy perturbation method. The obtained results are compared with Sumudu decomposition method. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is computationally very attractive.

scholarly journals An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
A. Kılıçman
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Efficient Approach ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Dym Equation ◽  
Harry Dym Equation

An efficient approach based on homotopy perturbation method by using sumudu transform is proposed to solve nonlinear fractional Harry Dym equation. This method is called homotopy perturbation sumudu transform (HPSTM). Furthermore, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement, and, hence, this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the HPSTM show that the approach is easy to implement and computationally very attractive.

scholarly journals Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Saeed Dinarvand ◽  
Abed Moradi
Keyword(s):  
Shooting Method ◽  
Homotopy Perturbation Method ◽  
Viscous Incompressible Fluid ◽  
Axisymmetric Flow ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Homotopy Perturbation ◽  
Two Dimensional Flow ◽  
Squeeze Number ◽  
Flow Case

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates for two cases, the two-dimensional flow case and the axisymmetric flow case, is investigated. The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). Graphical results are presented to investigate the influence of the squeeze number on the velocity, skin friction, and pressure gradient. The validity of our solutions is verified by the numerical results obtained by shooting method, coupled with Runge-Kutta scheme.

scholarly journals Analytic and Approximate Solutions of the Space-Time Fractional Schrödinger Equations by Homotopy Perturbation Sumudu Transform Method

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Sara H. M. Hamed ◽  
Eltayeb A. Yousif ◽  
Arbab I. Arbab
Keyword(s):  
Fractional Derivatives ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractional Schrödinger Equations ◽  
Sumudu Transform ◽  
Fractional Nonlinear Schrödinger Equation

A combination of homotopy perturbation method and Sumudu transform is applied to find exact and approximate solution of space and time fractional nonlinear Schrödinger equation. The fractional derivatives are described in the Caputo sense. The solutions are given in the form of convergent series with easily computable components. The results show that the method is effective and convenient for solving nonlinear differential equations of fractional order.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

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