scholarly journals Numerical Approximation for Nonlinear Gas Dynamic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hossein Aminikhah ◽  
Ali Jamalian
Keyword(s):  
Laplace Transform ◽  
Closed Form ◽  
Dynamic Equation ◽  
Numerical Approximation ◽  
Perturbation Methods ◽  
High Accuracy ◽  
The Other ◽  
Combined Method ◽  
Homotopy Perturbation ◽  
Gas Dynamic

Laplace transform and new homotopy perturbation methods are adopted to study gas dynamic equation analytically. The solutions introduced in this study can be used to obtain the closed form of the solutions if they are required. The combined method needs less work in comparison with the other homotopy perturbation methods and decreases volume of calculations considerably. Results show that the new method is more effective and convenient to use, and is high accuracy evident.

scholarly journals A New Efficient Method for Nonlinear Fisher-Type Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hossein Aminikhah ◽  
Farshid Mehrdoust ◽  
Ali Jamalian
Keyword(s):  
Laplace Transform ◽  
Closed Form ◽  
Efficient Method ◽  
Perturbation Methods ◽  
High Accuracy ◽  
The Other ◽  
New Method ◽  
Combined Method ◽  
Homotopy Perturbation

Laplace transform and new homotopy perturbation methods are adopted to study Fisher-type equations analytically. The solutions introduced in this study can be used to obtain the closed form of the solutions if they are required. The combined method needs less work in comparison with the other homotopy perturbation methods and decreases volume of calculations considerably. The method is tested on various examples, and results show that new method is more effective and convenient to use, and high accuracy of it is evident.

scholarly journals Analytical Approximation to the Solution of Nonlinear Blasius’ Viscous Flow Equation by LTNHPM

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hossein Aminikhah
Keyword(s):  
Laplace Transform ◽  
Viscous Flow ◽  
Numerical Method ◽  
Perturbation Methods ◽  
Analytical Approximation ◽  
High Accuracy ◽  
Flow Equation ◽  
New Method ◽  
Homotopy Perturbation

Laplace transform and new homotopy perturbation methods are adopted to study Blasius’ viscous flow equation analytically. The solutions approximated by the proposed method are shown to be precise as compared to the corresponding results obtained by Howarth’s numerical method. A high accuracy of the new method is evident.

Solution of the Black-Scholes Equation for Pricing of Barrier Option

2011 ◽  
Vol 66 (5) ◽  
pp. 289-296 ◽  
Author(s):  
Mehdi Dehghan ◽  
Somayeh Pourghanbar
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Perturbation Methods ◽  
Terminal Condition ◽  
Initial Condition ◽  
Barrier Option ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Black Scholes ◽  
Computational Work

In this paper two different methods are presented to approximate the solution of the Black-Scholes equation for valuation of barrier option. These techniques can be applied directly for all types of differential equations, homogeneous or inhomogeneous. The use of these methods provides the solution of the problem in a closed form while the mesh point techniques provide the approximation at mesh points only. Also, the two schemes need less computational work in comparison with the traditional methods. These techniques can be employed for problems with initial condition. In this paper we use the variational iteration and homotopy perturbation methods for solving the Black-Scholes equation with terminal condition. Numerical results are compared with theoretical solutions in order to confirm the validity of the presented procedures.

Solutions of the Singular IVPs of Lane-Emden type equations by combining Laplace transformation and perturbation technique

2018 ◽  
Vol 7 (4) ◽  
pp. 273-278 ◽  
Author(s):  
Hossein Aminikhah
Keyword(s):  
Laplace Transform ◽  
Efficient Method ◽  
Initial Value Problems ◽  
Laplace Transformation ◽  
Perturbation Methods ◽  
Perturbation Technique ◽  
Initial Value ◽  
Homotopy Perturbation ◽  
Polynomial Series ◽  
Linear And Nonlinear

AbstractIn this paper, we propose an efficient method to solve linear and nonlinear singular initial value problems of Lane-Emden type equations by combining Laplace transformation and homotopy perturbation methods. The method is based upon Laplace transform, polynomial series and perturbation technique. Several examples, including some well-known Lane-Emden problems, are presented to show the ability and accuracy of the modify method.

Approximate analytical solution for the one-dimensional nonlinear Boussinesq equation

2015 ◽  
Vol 25 (4) ◽  
pp. 831-840 ◽  
Author(s):  
Hossein Aminikhah
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Arbitrary Function ◽  
Perturbation Methods ◽  
Boussinesq Equation ◽  
Approximate Solutions ◽  
Content Type ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
The One

Purpose – The purpose of this paper is to provide closed-form approximate solutions to the one-dimensional Boussinesq equation for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function of time. Combination of the Laplace transform and homotopy perturbation methods (LTHPM) are considered as an algorithm which converges rapidly to the exact solution of the nonlinear Boussinesq equation. Design/methodology/approach – The authors present the solution of nonlinear Boussinesq equation by combination of Laplace transform and new homotopy perturbation methods. An important property of the proposed method, which is clearly demonstrated in example, is that spectral accuracy is accessible in solving specific nonlinear nonlinear Boussinesq equation which has analytic solution functions. Findings – The authors proposed a combination of Laplace transform method and homotopy perturbation method to solve the one-dimensional Boussinesq equation. The results are found to be in excellent agreement. The results show that the LTNHPM is an effective mathematical tool which can play a very important role in nonlinear sciences. Originality/value – The authors provide closed-form approximate solutions to the one-dimensional Boussinesq equation for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function of time. In this work combination of Laplace transform and new homotopy perturbation methods (LTNHPM) are considered as an algorithm which converges rapidly to the exact solution of the nonlinear Boussinesq equation.

scholarly journals Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yanqin Liu
Keyword(s):  
Approximate Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Transformation Method ◽  
High Accuracy ◽  
Homotopy Perturbation ◽  
He’S Polynomials

A homotopy perturbation transformation method (HPTM) which is based on homotopy perturbation method and Laplace transform is first applied to solve the approximate solution of the fractional nonlinear equations. The nonlinear terms can be easily handled by the use of He's polynomials. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

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