scholarly journals Solution of the Black-Scholes Equation: LDM and SDM

2021 ◽  
Vol 23 (07) ◽  
pp. 1111-1115
Author(s):  
R. K. Pavan Kumar. Pannala ◽  
Keyword(s):  
Differential Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Decomposition Methods ◽  
Financial Mathematics ◽  
Discretization Method ◽  
Discretization Methods ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Laplace Decomposition Method

The main aim of this paper is to discuss a new way of a non-discretization method for the solution of the Black-Scholes equation. Black-Scholes is a mathematical model based on a partial differential equation. The solution of the model is of utmost importance in financial mathematics to estimate option pricing. Several analytical, numerical, and non-discretization methods are existing in the literature to solve the model. Two decomposition methods namely the Laplace decomposition method (LDM) and Sumudu decomposition method (SDM) are adopted for the present study. The results of the present techniques have closed an agreement with an approximate solution which has been obtained with the help of the Adomian Decomposition Method (ADM).

scholarly journals Penerapan Metode Dekomposisi Adomian Laplace Dalam Menentukan Solusi Persamaan Panas

2019 ◽  
Vol 1 (2) ◽  
pp. 206
Author(s):  
Muhammad Abdy ◽  
Syafruddin Side ◽  
Reza Arisandi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Equation ◽  
Laplace Transform ◽  
Calculation Result ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

Abstrak. Artikel ini membahas tentang penerapan Metode Dekomposisi Adomian Laplace (LADM) dalam menentukan  solusi  persamaan panas. Metode Dekomposisi Adomian Laplace merupakan metode semi analitik untuk menyelesaikan persamaan diferensial nonlinier yang mengkombinasikan antara tranformasi Laplace dan metode dekomposisi Adomian. Berdasarkan hasil perhitungan, metode dekomposisi Adomian Laplace dapat menghampiri penyelesaian persamaan diferensial biasa nonlinear.Kata kunci: Metode Dekomposisi Adomian Laplace, Persamaan Diferensial Parsial, Persamaan PanasAbstract. This study discusses the application of Adomian Laplace Decomposition Method (ALDM) in determining the solution of heat equation. Adomian Laplace Decomposition Method is a semi analytical method to solve nonlinear differential equations that combine Laplace transform and Adomian decomposition method. Based on the calculation result, Adomian Laplace decomposition method can approach the settlement of ordinary nonlinear differential equations.Keywords: Adomian Laplace Decomposition Method, Partial Differential Equation, Heat Equation.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

scholarly journals On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668653 ◽  
Author(s):  
Hassan Eltayeb Gadain ◽  
Imed Bachar
Keyword(s):  
Parabolic Equation ◽  
Laplace Transform ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

AN APPROPRIATE APPROACH TO PRICING EUROPEAN-STYLE OPTIONS WITH THE ADOMIAN DECOMPOSITION METHOD

2018 ◽  
Vol 59 (3) ◽  
pp. 349-369
Author(s):  
ZIWIE KE ◽  
JOANNA GOARD ◽  
SONG-PING ZHU
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
European Options ◽  
Black Scholes Model ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Digital Options ◽  
Continuous Estimation

We study the numerical Adomian decomposition method for the pricing of European options under the well-known Black–Scholes model. However, because of the nondifferentiability of the pay-off function for such options, applying the Adomian decomposition method to the Black–Scholes model is not straightforward. Previous works on this assume that the pay-off function is differentiable or is approximated by a continuous estimation. Upon showing that these approximations lead to incorrect results, we provide a proper approach, in which the singular point is relocated to infinity through a coordinate transformation. Further, we show that our technique can be extended to pricing digital options and European options under the Vasicek interest rate model, in both of which the pay-off functions are singular. Numerical results show that our approach overcomes the difficulty of directly dealing with the singularity within the Adomian decomposition method and gives very accurate results.

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.

Sign in / Sign up

Export Citation Format

Share Document