The Study Of The Numerical Solution Based On Adomain Decomposition Of The Black-scholes Equation

Options as one of the highlights problems in researching financial andeconomic in the current world, to cause the attention of more and more people. Theoption pricing as the core issue of study options, have also made remarkableachievements. In recent years, with the rapid development of economy, increasinglycomplex options, pricing methods also emerge in endlessly. Black-Scholes equation asone of the most effective equation describing option pricing, the solving problem isalways the focus of people’s attention.Since the1970s, emerged a large number ofmethods for solving the differential equation of flops, but most of these methods canonly be applicable to the Black-Scholes equation in a form, when the equation of acoefficient changes, so the validity of this method will lose the original.So, manyscholars are also trying to find a way to apply Black-Scholes equation of variablecoefficient, and to make the numerical solution to achieve high precision.Adomain decomposition method was proposed and developed by themathematical physicist George Adomain and it is also known as inverse operatormethod.As to solve the linear and nonlinear mathematical physics equationapproximate analytical solution of a kind of new method, it has good convergence, andeasy to calculate.This article is on the basis of the Adomain decomposition method, the researchwith the final conditions depend on the time and space and the coefficient ofinhomogeneous Black-Scholes equation, first of all, we get it contains operator formiterative general series solution; Then analysis respectively in constant coefficient,coefficient of space and time correlation and coefficient and time are related cases,Black-Scholes equation operator series solution problem. Finally, we analyze thismethod, the accuracy of the equations. We randomly as the coefficient of function ofnegative, and then calculate the accurate solution of equation and the series solution,compare the two errors. Through analysis and comparison, will find that the equationbetween the numerical solution and exact solution of error will reduce with the increaseof the number of iterations, proves Adomain decomposition method for solvingnonhomogeneous Black-Scholes equation numerical solution of the problem is veryeffective.The end of this article is the use of Adomain decomposition method, and findmore suitable for solving inhomogeneous Black-Scholes equation numerical solution method.