Cubic spline iterative method for Poisson's equation in cylindrical polar coordinates
Summary: Using a non-polynomial 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.
scientific article; zbMATH DE number 6014687
scientific article