scholarly journals An approximate-analytical solution for the Hamilton–Jacobi–Bellman equation via homotopy perturbation method

2012 ◽  
Vol 36 (11) ◽  
pp. 5614-5623 ◽  
Author(s):  
H. Saberi Nik ◽  
S. Effati ◽  
M. Shirazian
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Bellman Equation ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Homotopy Perturbation ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

scholarly journals On the Hamilton-Jacobi-Bellman Equation by the Homotopy Perturbation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Aden Ahmed ◽  
Suares Clovis Oukouomi Noutchie
Keyword(s):  
Exact Solution ◽  
Perturbation Method ◽  
Decomposition Method ◽  
Bellman Equation ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Homotopy Decomposition ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

Our concern in this paper is to use the homotopy decomposition method to solve the Hamilton-Jacobi-Bellman equation (HJB). The approach is obviously extremely well organized and is an influential procedure in obtaining the solutions of the equations. We portrayed particular compensations that this technique has over the prevailing approaches. We presented that the complexity of the homotopy decomposition method is of orderO(n). Furthermore, three explanatory examples established good outcomes and comparisons with exact solution.

scholarly journals An Approximate Analytical Solution Of Nonlinear Equations In N-Aminopiperidine Synthesis: New Approach Of Homotopy Perturbation Method)

2021 ◽  
Vol 12 (1S) ◽  
pp. 595-605
Author(s):  
R. Joy Salomi, Et. al.
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Rate Equations ◽  
Simple Analytical Expression ◽  
New Approach ◽  
Homotopy Perturbation ◽  
Numerical Result

the synthesis of N-aminopiperidine (NAPP) using hydroxylamine-O-sulfonic acid (HOSA) is based on system of nonlinear rate equations. The new approach to homotopy perturbation method is applied to solve the nonlinear equations. A simple analytical expression for concentrations of hydroxylamine-O-sulfonique acid (HOSA), piperidine (PP), N-aminopiperidine (NAPP), sodium hydroxide (NaOH) and diazene (N2H2) along with NAPP yield is obtained and is compared with numerical result. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation. The obtained analytical result of NAPP yield is compared with the experimental results. The influence of reagents ratio p and rate constants ratio r on yield has been discussed.

scholarly journals Approximate analytical solution for Phi-four equation with he’s fractal derivative

2021 ◽  
pp. 127-127
Author(s):  
Shuxian Deng ◽  
Xinxin Ge
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Integral Transform ◽  
Approximate Analytical Solution ◽  
Homotopy Perturbation ◽  
Fractal Derivative ◽  
Fractal Differential Equations ◽  
First Time

This paper, for the first time ever, proposes a Laplace-like integral transform, which is called as He-Laplace transform, its basic properties are elucidated. The homotopy perturbation method coupled with this new transform becomes much effective in solving fractal differential equations. Phi-four equation with He?s derivative is used as an example to reveal the main merits of the present technology.

scholarly journals Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
European Option ◽  
European Option Pricing ◽  
Homotopy Perturbation ◽  
Black Scholes ◽  
Sumudu Transform

The homotopy perturbation method, Sumudu transform, and He’s polynomials are combined to obtain the solution of fractional Black-Scholes equation. The fractional derivative is considered in Caputo sense. Further, the same equation is solved by homotopy Laplace transform perturbation method. The results obtained by the two methods are in agreement. The approximate analytical solution of Black-Scholes is calculated in the form of a convergence power series with easily computable components. Some illustrative examples are presented to explain the efficiency and simplicity of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document