scholarly journals Modified Laplace Decomposition Method for Lane-Emden Type Differential Equations

2013 ◽  
pp. 98-102 ◽  
Author(s):  
Fu-Kang Yin ◽  
Wang-Yi Han ◽  
Jun-Qiang Song
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Laplace Decomposition Method

scholarly journals Laplace Decomposition Method for Solving Fractional Black-Scholes European Option Pricing Equation

2020 ◽  
Vol 1 (4) ◽  
pp. 194-207
Author(s):  
Abiodun Ezekiel Owoyemi ◽  
Ira Sumiati ◽  
Endang Rusyaman ◽  
Sukono Sukono
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Option Pricing ◽  
Decomposition Method ◽  
European Option ◽  
Partial Differential ◽  
European Option Pricing ◽  
Black Scholes ◽  
Pricing Problems ◽  
Laplace Decomposition Method

Fractional calculus is related to derivatives and integrals with the order is not an integer. Fractional Black-Scholes partial differential equation to determine the price of European-type call options is an application of fractional calculus in the economic and financial fields. Laplace decomposition method is one of the reliable and effective numerical methods for solving fractional differential equations. Thus, this paper aims to apply the Laplace decomposition method for solving the fractional Black-Scholes equation, where the fractional derivative used is the Caputo sense. Two numerical illustrations are presented in this paper. The results show that the Laplace decomposition method is an efficient, easy and very useful method for finding solutions of fractional Black-Scholes partial differential equations and boundary conditions for European option pricing problems.

scholarly journals Yang-Laplace Decomposition Method for Nonlinear System of Local Fractional Partial Differential Equations

2019 ◽  
Vol 4 (2) ◽  
pp. 489-502 ◽  
Author(s):  
Djelloul Ziane ◽  
Mountassir Hamdi Cherif ◽  
Carlo Cattani ◽  
Kacem Belghaba
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Decomposition Method ◽  
Differential Operators ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Computational Work ◽  
Laplace Decomposition Method

AbstractThe basic motivation of the present study is to extend the application of the local fractional Yang-Laplace decomposition method to solve nonlinear systems of local fractional partial differential equations. The differential operators are taken in the local fractional sense. The local fractional Yang-Laplace decomposition method (LFLDM) can be easily applied to many problems and is capable of reducing the size of computational work to find non-differentiable solutions for similar problems. Two illustrative examples are given, revealing the effectiveness and convenience of the method.

scholarly journals Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula

2018 ◽  
Vol 11 (1) ◽  
pp. 202 ◽  
Author(s):  
Dimple Rani ◽  
Vinod Mishra
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Newton Raphson ◽  
Laplace Decomposition Method ◽  
Adomian Polynomial

In this paper, we establish a modified Laplace decomposition method for nonlinear volterra integral and integro-differential equations. This technique differs from the general Laplace decomposition method because of the terms involved in Adomian polynomial.We have used Newton Raphson formula in place of the $u_{i}$ in Adomian polynomial. The proposed scheme is investigated with some illustrative examples and has given reliable results.

scholarly journals Laplace Decomposition Method for Solving Fractional Black-Scholes European Option Pricing Equation

2020 ◽  
Vol 1 (4) ◽  
pp. 194-207
Author(s):  
Abiodun Ezekiel Owoyemi ◽  
Ira Sumiati ◽  
Endang Rusyaman ◽  
Sukono Sukono
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Option Pricing ◽  
Decomposition Method ◽  
European Option ◽  
Partial Differential ◽  
European Option Pricing ◽  
Black Scholes ◽  
Pricing Problems ◽  
Laplace Decomposition Method

Fractional calculus is related to derivatives and integrals with the order is not an integer. Fractional Black-Scholes partial differential equation to determine the price of European-type call options is an application of fractional calculus in the economic and financial fields. Laplace decomposition method is one of the reliable and effective numerical methods for solving fractional differential equations. Thus, this paper aims to apply the Laplace decomposition method for solving the fractional Black-Scholes equation, where the fractional derivative used is the Caputo sense. Two numerical illustrations are presented in this paper. The results show that the Laplace decomposition method is an efficient, easy and very useful method for finding solutions of fractional Black-Scholes partial differential equations and boundary conditions for European option pricing problems.

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