JFNK Method Of Solving Non-linear Black-Scholes Equation

This paper deals with ID nonlinear Black-Scholes option pricing model; Evaluation relevant to the non-linear model is often done in numerical computation, usually by means of the difference methods. we form the Crank-Nicolson scheme and implicit scheme. Meanwhile the stability analysis of the scheme is presented. Now the biggest need in the famous finite difference scheme is for increased speed. We employ the Jacobian-Free Newton Krylov technique to achieve a difference method. The JFNK method pays as much attention to memory traffic as to the actual amount of arithmetic. The JFNK method is executed to solve the nonlinear Black-Scholes model. The comparison between the numerical solution by JFNK method to the nonlinear Black-Scholes model and the solution to famous (linear) Black-Scholes equation is illustrated. It shows that this method is efficient.