scholarly journals Analytical solutions of convection–diffusion problems by combining Laplace transform method and homotopy perturbation method

2015 ◽  
Vol 54 (3) ◽  
pp. 645-651 ◽  
Author(s):  
Sumit Gupta ◽  
Devendra Kumar ◽  
Jagdev Singh
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Convection Diffusion ◽  
Homotopy Perturbation ◽  
Diffusion Problems

scholarly journals A New Efficient Method for Solving Two-Dimensional Burgers' Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Hossein Aminikhah
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Efficient Method ◽  
Homotopy Perturbation Method ◽  
Burgers Equation ◽  
Two Dimensional ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform

We introduce a new hybrid of the Laplace transform method and new homotopy perturbation method (LTNHPM) that efficiently solves nonlinear two-dimensional Burgers’ equation. Three examples are given to demonstrate the efficiency of the new method.

scholarly journals Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics Equation

2012 ◽  
Vol 8 (1) ◽  
pp. 55-61 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
Keyword(s):  
Laplace Transform ◽  
Gas Dynamics ◽  
Homotopy Perturbation Method ◽  
Nonlinear Problems ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform ◽  
Gas Dynamics Equation ◽  
Adomian’S Polynomials

Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics EquationIn this paper, we apply a combined form of the Laplace transform method with the homotopy perturbation method to obtain the solution of nonlinear gas dynamics equation. This method is called the homotopy perturbation transform method (HPTM). This technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that this scheme solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method. The results reveal that the homotopy perturbation transform method (HPTM) is very efficient, simple and can be applied to other nonlinear problems.

Solution of Non-Linear RLC Circuit Equation Using the Homotopy Perturbation Transform Method

2021 ◽  
Vol 14 (1) ◽  
pp. 89-100
Keyword(s):  
Laplace Transform ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Rlc Circuit ◽  
Non Linear ◽  
The Laplace Transform

Abstract: In this paper, we apply the Homotopy Perturbation Transform Method (HPTM) to obtain the solution of Non-Linear RLC Circuit Equation. This method is a combination of the Laplace transform method with the homotopy perturbation method. The HPTM can provide analytical solutions to nonlinear equations just by employing the initial conditions and the nonlinear term decomposed by using the He’s polynomials. Keywords: Homotopy perturbation, Laplace transform, He’s polynomials, Non-linear RLC circuit equation.

Solution of Fifth-order Korteweg and de Vries Equation by Homotopy perturbation Transform Method using He’s Polynomial

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Dinkar Sharma ◽  
Prince Singh ◽  
Shubha Chauhan
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Present Scheme ◽  
Homotopy Perturbation ◽  
Kdv Equations ◽  
De Vries ◽  
The Laplace Transform ◽  
Fifth Order

AbstractIn this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He’s polynomials. Two test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM).

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 inverse Laplace homotopy technique for fractional heat equations

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 185-194 ◽  
Author(s):  
Mehmet Yavuz ◽  
Necati Ozdemir
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Heat Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Proposed Model ◽  
Fractional Pde ◽  
The Laplace Transform

In this paper, we have aimed the numerical inverse Laplace homotopy technique for solving some interesting 1-D time-fractional heat equations. This method is based on the Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method. Firstly, we have applied to the fractional 1-D PDE by using He?s polynomials. Then we have used Laplace transform method and discussed how to solve these PDE by using Laplace homotopy perturbation method. We have declared that the proposed model is very efficient and powerful technique in finding approximate solutions to the fractional PDE.

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.

scholarly journals An efficient approach for solution of fractional-order Helmholtz equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nehad Ali Shah ◽  
Essam R. El-Zahar ◽  
Mona D. Aljoufi ◽  
Jae Dong Chung
Keyword(s):  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Hybrid Technique ◽  
Science And Engineering ◽  
Helmholtz Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Suggested Technique ◽  
Present Technique

AbstractIn this article, a hybrid technique called the homotopy perturbation Elzaki transform method has been implemented to solve fractional-order Helmholtz equations. In the hybrid technique, the Elzaki transform method and the homotopy perturbation method are amalgamated. Three problems are solved to validate and demonstrate the efficacy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the results by other techniques. It is shown that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering.

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