THIRD ORDER ITERATIVE METHOD FOR SOLVING NON-LINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION IN FINANCIAL APPLICATION

In this paper, a third-order iterative scheme is presented for searching approximate solutions of a non-linear parabolic partial differential equation to simulate the elaboration of interest rates in the fanatical application. First, by using Taylor series expansion we gain the discretization scheme for the model problem. Then, using the Gauss-Seidel iterative scheme we solve the proposed model problems. To validate the convergences of the proposed numerical techniques, three model illustrations are considered. The convergent analysis of the present techniques is worked by supporting the theoretical and fine numerical statements. The accuracy of the present numerical techniques has been measured by using average absolute error root mean square error and point-wise maximum absolute error. Then, we compare these get crimes with the result attained in the literature. These results are also presented in tables and graphs. The comparison of physical behavior between present numerical versus its exact solutions is also presented in terms of graphs. As we can see from the table and graphs, the present numerical techniques approximate the exact result veritably well. So, it is relatively effective for simulating fanatical application to the non-linear parabolic partial differential equation.