A reliable treatment of residual power series method for time-fractional Black–Scholes European option pricing equations

Dubey, Ved Prakash; Kumar, Rajneesh; Kumar, Devendra

doi:10.1016/j.physa.2019.122040

Cited by 39 publications

(17 citation statements)

References 39 publications

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“…As the crux of RPSM is differentiation of an infinite (multiple) power series (since differentiation is relatively an easier task than integration) along with the advantages of no linearization/transformation, no discretization/round-off errors, and direct application to the given problem by choosing approximation value/function. These features make RPSM as the method of choice for a wider class of ODE and PDE problems of mathematical and physical sciences (Dubey et al, 2019;Kumar et al, 2016aKumar et al, , 2017Kumar et al, , 2016bAlquran et al, 2020;Haq and Hussain, 2018).…”

Section: Introductionmentioning

confidence: 99%

An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

Hussain

Farooq

Ghafoor

2022

Preprint

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This article proposes a simple yet efficient/powerful iterative scheme to obtain approximate solutions to a class of nonlinear parabolic partial differential equations. The approximation method is based on the residual error function and the multiple power series expansion. Error estimates are derived and convergence of the proposed method is established. Several numerical examples are then considered to validate the theoretical results and highlight the computational ease of the developed residual power series method on multi-dimensional nonlinear Burgers’ equations. It is observed that the proposed approximation method captures shock wave propagation and steep gradient formation very well, and delivers more accurate results than the contemporary methods in higher dimensions.

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Section: Introductionmentioning

confidence: 99%

An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

Hussain

Farooq

Ghafoor

2022

Preprint

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“…Sunil Kumar et al have used the homotopy perturbation method for solving Black–Scholes equation 25 . In Dubey et al, 26 the authors provided a residual power series method for time‐fractional Black–Scholes equation. Choi and Choi 27 have proposed a Hermite polynomials method for solving Black–Scholes boundary‐value problem.…”

Section: Introductionmentioning

confidence: 99%

Solving fractional Black–Scholes equation by using Boubaker functions

Khajehnasiri

Safavi

2021

Math Methods in App Sciences

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The fractional Black–Scholes pricing model widely appears in financial markets. This paper presents the special class of operational matrix to approximate the solution of fractional Black–Scholes equation based on the Boubaker polynomial functions. The Boubaker operational matrix of the fractional derivative converts the model to obtain the numerical solution of the time‐fractional Black–Scholes equation. The numerical results are displayed in some tables for better illustration with testing in some examples.

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“…Singh et al [60] have explored the new features of fractional Biswas-Milovic model with Mittag-Leffler kernel. In 2019, fractional Black-Scholes equations have been studied via RPSM by Dubey et al [61].…”

Section: Introductionmentioning

confidence: 99%

An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

Dubey

Kumar²,

Kumar

et al. 2020

Adv Differ Equ

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In this paper, we broaden the utilization of a beautiful computational scheme, residual power series method (RPSM), to attain the fractional power series solutions of nonhomogeneous and homogeneous nonlinear time-fractional systems of partial differential equations. This paper considers the fractional derivatives of Caputo-type. The approximate solutions of given systems of equations are calculated through the utilization of the provided initial conditions. This iterative scheme generates the fast convergent series solutions with conveniently determinable components. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability and easiness regarding the procedure of the solution, as well as its better approximation. The repercussions of the fractional order of Caputo derivatives on solutions are depicted through graphical presentations for various particular cases.

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A reliable treatment of residual power series method for time-fractional Black–Scholes European option pricing equations

Cited by 39 publications

References 39 publications

An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

Solving fractional Black–Scholes equation by using Boubaker functions

An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

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