scholarly journals Extension of the Sumudu homotopy perturbation method to an attractor for one-dimensional Keller–Segel equations

2015 ◽  
Vol 39 (10-11) ◽  
pp. 2909-2916 ◽  
Author(s):  
Abdon Atangana
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
One Dimensional ◽  
Homotopy Perturbation

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.

APPLICATION OF HOMOTOPY PERTURBATION METHOD TO THE MATHEMATICAL MODELLING OF TEMPERATURE RISE DURING MICROWAVE HYPERTHERMIA

2021 ◽  
Vol 5 (2) ◽  
pp. 273-282
Author(s):  
Erinle-Ibrahim L. Morenikeji ◽  
Ayeni O. Babatunde ◽  
Idowu K Oluwatobi
Keyword(s):  
Thermal Conductivity ◽  
Cancer Therapy ◽  
Perturbation Method ◽  
Microwave Heating ◽  
Homotopy Perturbation Method ◽  
Blood Perfusion ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Maximum Rise ◽  
Microwave Hyperthermia

We study a one dimensional non-linear model of multi-layered human skin exposed to microwave heating during cancer therapy. The model is analyzed using homotopy perturbation method and the fact that there are variations in specific heat, thermal conductivity and blood perfusion from one individual to another were considered. The purpose of this study was to investigate the effect of variable blood perfusion, microwave heating and thermal conductivity on the temperature field during microwave hyperthermia. By varying the parameters, we were able to determine maximum rise of temperature as an individual undergoes cancer therapy. The results were presented in graphs and it was discovered that the temperature of the tumor increases with increase in the microwave heating index while the blood perfusion remain constant.

NUMERICAL SOLUTIONS OF WAVE EQUATIONS SUBJECT TO AN INTEGRAL CONSERVATION CONDITION BY HE'S HOMOTOPY PERTURBATION METHOD

2011 ◽  
Vol 25 (32) ◽  
pp. 4457-4469 ◽  
Author(s):  
AHMET YILDIRIM ◽  
YAǦMUR GÜLKANAT
Keyword(s):  
Perturbation Method ◽  
Wave Equations ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Conservation Condition ◽  
Direct Problems

The aim of this paper is to solve one-dimensional wave equations that combine classical and integral boundary conditions using the homotopy perturbation method (HPM). The studied equations are changed into direct problems easy to be handled by the homotopy perturbation method. Several examples are given and the results are compared with exact solutions, revealing effectiveness and simplicity of the method.

Homotopy Perturbation Method for One-Dimensional Hyperbolic Equation with Integral Conditions

2010 ◽  
Vol 65 (12) ◽  
pp. 1077-1080 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yıldırım ◽  
Yasemin Kaplan
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Convergent Series ◽  
Hyperbolic Partial Differential Equations ◽  
One Dimensional ◽  
Local Boundary ◽  
Homotopy Perturbation

In this study, we use the homotopy perturbation method (HPM) to solve an initial-boundary value problem with a non-classic condition for the one-dimensional wave equation.We will deal with a new type of non-local boundary value problems which are the solution of hyperbolic partial differential equations with a non-standard boundary specification. The method is very reliable and effective and provides the solution in terms of rapid convergent series. Several examples are tested to support our study.

scholarly journals Aboodh Homotopy Perturbation Method of solving Burgers Equation.

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Oludapo Omotola Olubanwo ◽  
Olutunde Samuel Odetunde ◽  
Adetoro Temitope Talabi
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Burgers Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
High Accuracy ◽  
Partial Differential ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Laplace Decomposition Method

In this paper, we present a reliable combination of Aboodh Transform and Homotopy perturbation method to determine the exact solution of one dimensional Burgers equation which is a nonlinear partial differential equation. Some cases of one dimensional nonlinear partial differential equations are considered to illustrate the capability and reliability of Aboodh Homotopy perturbation method. We have compared the analytical solution obtained with the available Laplace decomposition method. The solution which is found to be exactly the same. The result revealed that the combination of the Aboodh Transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems. The method is tested on three examples and results show that the new method is more effective and convenient to use and high accuracy of it is evident.

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. 

Sign in / Sign up

Export Citation Format

Share Document