Third Order Iterative Method for Solving Non-Linear Parabolic Partial Differential Equation in Financial Application

Abstract

In this paper, third order iterative scheme is presented for working the solution the non-linear stochastic parabolic equation in one dimensional space. First, the given result sphere is discretized by using invariant discretization grid point. Next, by using Taylor series expansion we gain the discretization of the model problem. From this, we gain the system of nonlinear ordinary difference equations. By rearranging this scheme, we gain iterative schemes which is called gauss Jacobean iterative scheme. To validate the convergences of the proposed system, three model illustrations are considered and answered it at each specific grid point on its result sphere. The coincident (convergent) analysis of the present techniques is worked by supported the theoretical and fine statements and the delicacy of the result is attained. The delicacy of the present techniques has been shown in the sense of average absolute error (AAE), root mean square error norm and point-wise maximum absolute error norm and comparing gets crimes in the result attained in literature and these results are also presented in tables and graphs. The physical gets of results between numerical versus are also been presented in terms of graphs. As we can see from the table and graphs, the present system approach are approximates the exact result veritably well and it's relatively effective and virtually well suited for working the solution for non-linear parabolic equation.