Cubic Spline Iterative Method for Poisson’s Equation in Cylindrical Polar Coordinates

Abstract EN

Using nonpolynomial cubic spline approximation in x- and finite difference in y-direction, we discuss a numerical approximation of O(k2+h4) for the solutions of diffusion-convection equation, where k>0 and h>0 are grid sizes in y- and x-coordinates, respectively.

We also extend our technique to polar coordinate system and obtain high-order numerical scheme for Poisson’s equation in cylindrical polar coordinates.

Iterative method of the proposed method is discussed, and numerical examples are given in support of the theoretical results.