Polynomial differential quadrature method for numerical solution of the generalized Black-Scholes ‎equation

Document Type : Original Article

Authors
Zahra Sarvari 1
Mojtaba Ranjbar 2
Shahram Rezapour 1
1 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
2 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran. Faculty of Finance Sciences, Kharazmi University, Tehran, Iran.
10.22034/maco.2.1.12
Abstract
In this paper‎, ‎the polynomial differential quadrature method (PDQM) is implemented to find the numerical solution of the generalized Black-Scholes partial differential equation‎. ‎The PDQM reduces the problem into a system of first order non-linear differential equations and then‎, ‎the obtained system is solved by optimal four-stage‎, ‎order three strong stability-preserving time-stepping Runge-Kutta (SSP-RK43) scheme‎. ‎Numerical examples are given to illustrate the efficiency of the proposed method‎.

Keywords

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Mathematical Analysis and Convex Optimization
Volume 2, Issue 1
June 2021
Pages 119-130