Modified Homotopy Perturbation Transform Method: A Paradigm for Nonlinear Boundary Layer Problems

2014 ◽  
Vol 15 (1) ◽  
Author(s):  
Yasir Khan ◽  
Muhammad Usman
Keyword(s):  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Boundary Layer Problems

scholarly journals Solving Boundary-Layer Problems by Residual-Power-Series Method

2016 ◽  
Vol 8 (3) ◽  
pp. 68
Author(s):  
Mohd Taib Shatnawi
Keyword(s):  
Boundary Layer ◽  
Power Series ◽  
Nonlinear Boundary ◽  
Power Series Method ◽  
Boundary Layer Equations ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Linear And Nonlinear ◽  
Boundary Layer Problems ◽  
Residual Power

<p><span lang="EN-US">In this paper, the so-called residual-power-series (RPS) method is presented for solving nonlinear boundary-layer equations. The RPS method provides a single unified treatment for the linear and nonlinear terms in the equations. The accuracy and efficiency of the RPS method is demonstrated for both a single and a system of two coupled boundary-layer equations on an unbounded domain.</span></p>

scholarly journals Radiation Effects on Two-Dimensional MHD Falkner-Skan Wedge Flow

2015 ◽  
Vol 773-774 ◽  
pp. 368-372 ◽  
Author(s):  
M. Abdulhameed ◽  
Habibi Saleh ◽  
Ishak Hashim ◽  
Rozaini Roslan
Keyword(s):  
Boundary Layer ◽  
Radiation Effects ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Fluid Temperature ◽  
Two Dimensional ◽  
Wedge Flow ◽  
Boundary Layer Equations ◽  
Homotopy Perturbation ◽  
The Magnetic Field

Radiation effects on two-dimensional MHD Falkner-Skan boundary layer wedge have been studied. Analytical solution of nonlinear boundary-layer equations is obtained by modified homotopy perturbation method. It is observed that the magnetic field tends to decelerate fluid flow whereas radiations and thermal diffusion tend to increase fluid temperature.

Quasilinearization and Nonlinear Boundary-Layer Problems

Physics Today ◽  
1966 ◽  
Vol 19 (4) ◽  
pp. 98-101 ◽  
Author(s):  
Richard E. Bellman ◽  
Robert E. Kalaba ◽  
T. Teichmann
Keyword(s):  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Boundary Layer Problems

Numerical Comparison of Methods for Solving Boundary Layer Problems in Hydrodynamics

2013 ◽  
Vol 284-287 ◽  
pp. 508-512
Author(s):  
Shih Hsiang Chang
Keyword(s):  
Boundary Layer ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Differential Transform Method ◽  
Numerical Comparison ◽  
Transform Method ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Differential Transform ◽  
Boundary Layer Problems

This paper presents a numerical comparison between the differential transform method and the modified Adomian decomposition method for solving the boundary layer problems arising in hydrodynamics. The results show that the differential transform method and modified Adomian decomposition method are easier and more reliable to use in solving this type of problem and provides accurate data as compared with those obtained by other numerical methods.

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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