Cubic Spline Approximation for Two Dimensional Non-Linear Elliptic Boundary Value Problems

This section exhibits a nine point reduced discretization of order two in y-and three in xbearings for the solution of two dimensional nonlinear elliptic boundary value problems on a non-uniform mesh using cubic spline approximations. We examine the total deduction strategy of the method in details and furthermore talk about how our discretization can handle Poisson’s equation in polar coordinates. Convergence of the method has been set up. Some physical examples and their numerical outcomes are given to legitimize the convenience of the proposed method. The second order elliptic equations are gotten as the consistent state solutions (as t → ∞) of the illustrative and wave equations. Solutions of these equations are of incredible significance in numerous fields of science, for example, electromagnetics, astronomy, heat transfer, fluid mechanics and so on the grounds that they may speak to a temperature, electric or attractive potential, and relocation for an elastic membrane.