Cubic Spline Iterative Method for Poisson's Equation in Cylindrical Polar Coordinates. (12th February 2012) - Mohanty, R. K.; Kumar, Rajive; Dahiya, Vijay
Abstract : Using nonpolynomial cubic spline approximation in x - and finite difference in y -direction, we discuss a numerical approximation of O ( k 2 + h 4 ) 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.