scholarly journals Comparison Differential Transform Method With Homotopy Perturbation Method For Nonlinear Integral Equations

2012 ◽  
Vol 05 (04) ◽  
pp. 288-296 ◽  
Author(s):  
Malihe Bagheri ◽  
Mahnaz Bagheri ◽  
Ebrahim Miralikatouli
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
Differential Transform Method ◽  
Nonlinear Integral Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Differential Transform

scholarly journals Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhoujin Cui ◽  
Zisen Mao ◽  
Sujuan Yang ◽  
Pinneng Yu
Keyword(s):  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Time Derivative ◽  
Differential Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Differential Transform ◽  
Reduced Differential Transform Method

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.

scholarly journals Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Reza Abazari ◽  
Adem Kılıçman
Keyword(s):  
Integral Equations ◽  
Numerical Study ◽  
Volterra Integral Equations ◽  
Differential Transform Method ◽  
The Other ◽  
Two Dimensional ◽  
Nonlinear Integral Equations ◽  
Transform Method ◽  
Engineering Sciences ◽  
Differential Transform

The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM), and compared with the differential transform method (DTM). The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.

scholarly journals Solving fuzzy $(1+ n)$-dimensional Burgers’ equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mawia Osman ◽  
Zengtai Gong ◽  
Altyeb Mohammed Mustafa ◽  
Hong Yang
Keyword(s):  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Burgers Equation ◽  
Adomian Decomposition Method ◽  
Differential Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Differential Transform

AbstractIn this paper, we study the comparison of fuzzy differential transform method (FDTM), fuzzy Adomian decomposition method (FADM), fuzzy homotopy perturbation method (FHPM), and fuzzy reduced differential transform method (FRDTM) to obtain the solutions of fuzzy $(1 + n)$ ( 1 + n ) -dimensional Burgers’ equation under gH-differentiability. We have investigated many new results to solve the above problem, and the methods have been implemented. The four illustrative numerical examples are presented to demonstrate the effectiveness of the proposed methods and also to demonstrate the efficiency and simplicity of the ways they were developed and derived. The results also show that the methods are powerful mathematical tools for solving fuzzy $(1 + n)$ ( 1 + n ) -dimensional Burgers’ equation.

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.

Sign in / Sign up

Export Citation Format

Share Document