Essay On Fourier Analysis

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In numerical analysis, explicit and implicit approaches are used to obtain numerical approximations of time dependent ordinary and partial differential equations. Fractional order differential equations are used widely for finance market analysis. Implicit solution methods require more computational efforts and are complex to program. In order to overcome these difficulties, explicit method for fractional order differential equation has been introduced which is one of the most recently developed areas in the world of finance. The main aim of this paper is to investigate stability of Fractional Explicit method for qth order time fractional Black-Schols equation by the well known Fourier analysis method and a numerical experiment is presented for comparison of European call option prices for different values of ‘q’.

Keywords— Fractional calculus; Fractional Explicit Method; stability; European call options; time fractional Black-Schols equation; Fourier analysis.
MSC 2010 No.: 26A33, 65M06, 65TXX.

Introduction

In Numerical analysis, the use of Fractional calculus is increasing day by day. The field of fractional calculus is not new for mathematicians. It is as old as in the year 1695 , when L’Hopital sent a letter to Leibniz asking him an important question about the order of the derivative, “ What would be the result if order of derivative is
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After introduction 1, the next section 2, will review the working of Fractional Explicit method. Section 3 is based on the stability analysis of the method. In section 4, there is a numerical experiment analyzing the performance of Fractional Explicit method for different values of ‘q’. Data for this experiment is taken from historical data section of NSE website of jet airways of the period from 1st November 2016 to 30th November 2016. Graphical representation is given for the more precise comparison. Finally in section 5 there is concluding remarks for the
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