An algorithm for Adomian decomposition method

The Adomian Decomposition Method (ADM) is applied to obtain a fast and reliable solution to the BlackScholes equation with boundary condition for a European option. We cast the problem of pricing a European option with boundary conditions in terms of a diffusion partial differential equation with homogeneous boundary condition in order to apply the ADM. The analytical solution of the equations is calculated in the form of an explicit series approximation.

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“…Equation 16 can be solved using a software, such as MATLAB or MAPLE [17]. Substituting 14 and 15 in the equation 13 we have,…”

Section: The Adomian Decomposition Methods (Adm)mentioning

confidence: 99%

Solution of the Black-Scholes equation via the Adomian decomposition method

Avila¹,

Estrella²,

Blanco

2013

International Journal of Applied Mathematical Research

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“…The method has been described very clearly in [34]. The non-linear differential equation is written as:…”

Section: Adomian Decomposition Methodsmentioning

confidence: 99%

Efficient solution of a vibration equation involving fractional derivatives

Pálfalvi

2010

International Journal of Non-Linear Mechanics

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Fractional order (or, shortly, fractional) derivatives are used in viscoelasticity since the late 1980's, and they grow more and more popular nowadays.However, their efficient numerical calculation is nontrivial, because, unlike integer-order derivatives, they require evaluation of history integrals in every time step. Several authors tried to overcome this difficulty, either by simplifying these integrals or by avoiding them. In this paper, the Adomian decomposition method is applied on a fractionally damped mechanical oscillator for a sine excitation, and the analytical solution of the problem is found. Also, a series expansion is derived which proves very efficient for calculations of transients of fractional vibration systems. Numerical examples are included.

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“…[11] constructed an algorithm for solving nonlinear equations based on Newton-Raphson method using Adomian decomposition approach. In an effort to extend the usefulness of Adomian's decomposition method into other areas of mathematics, [12] developed a technique for calculating Adomian's polynomials for nonlinear operators. [13] presented a method for the solution of homogeneous differential equations using Adomian's decomposition without noisy terms.…”

Section: Introductionmentioning

confidence: 99%

Adomian Decomposition Approach to the Solution of the Burger’s Equation

Akpan¹

2015

AJCM

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Adomian decomposition method is presented as a method for the solution of the Burger's equation, a popular PDE model in the fluid mechanics. The method is computationally simple in application. The approximate solution is obtained by considering only the first two terms of the decomposition in this paper. Numerical experimentation shows accuracy of a minimum error of order five for various space steps and coefficient of kinematic viscosity. The method is considered high in accuracy.

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An algorithm for Adomian decomposition method

Cited by 57 publications

References 15 publications

Solution of the Black-Scholes equation via the Adomian decomposition method

Solution of the Black-Scholes equation via the Adomian decomposition method

Efficient solution of a vibration equation involving fractional derivatives

Adomian Decomposition Approach to the Solution of the Burger’s Equation

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