scholarly journals Analytical solution of nonlinear Klein-Gordon equations with cubic nonlinearity by extended Adomian decomposition method

2021 ◽  
Keyword(s):  
Analytical Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Cubic Nonlinearity ◽  
Adomian Decomposition ◽  
Klein Gordon

scholarly journals The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 780-785 ◽  
Author(s):  
Sunday O. Edeki ◽  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Grace O. Akinlabi
Keyword(s):  
Analytical Solution ◽  
Option Pricing ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Asian Option ◽  
Pricing Model ◽  
Adomian Decomposition ◽  
Option Pricing Model ◽  
Option Model ◽  
High Level

Abstract The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions are in good agreement with those of Rogers & Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani & Ahmad (ScienceAsia, 39S: 2013, 67–69). The proposed method is highly recommended for analytical solution of other forms of Asian option pricing models such as the geometric put and call options, even in their time-fractional forms. The basic Greeks obtained are the Theta, Delta, Speed, and Gamma which will be of great help to financial practitioners and traders in terms of hedging and strategy.

Numerical Solution of Time-Fractional Klein–Gordon Equation by Using the Decomposition Methods

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Jafari
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Gordon Equation ◽  
Adomian Decomposition Method ◽  
Type Equation ◽  
Decomposition Methods ◽  
Adomian Decomposition ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We compare these methods and discuss the convergence of them. The obtained results reveal that these methods are very accurate and effective.

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