Solution of one-dimensional space- and time-fractional advection–dispersion equation by homotopy perturbation method

2017 ◽  
Vol 65 (2) ◽  
pp. 353-361 ◽  
Author(s):  
Mritunjay Kumar Singh ◽  
Ayan Chatterjee
Keyword(s):  
Perturbation Method ◽  
Dispersion Equation ◽  
Homotopy Perturbation Method ◽  
Dimensional Space ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Space And Time ◽  
Advection Dispersion

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.

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