Cubic Spline Iterative Method for Poisson's Equation in Cylindrical Polar Coordinates. (12th February 2012)

• Record Type: Journal Article
• Authors: Mohanty, R. K.; Kumar, Rajive; Dahiya, Vijay
• Other Names: Wallet J.-C. Academic Editor.; Zhou H. Academic Editor.
• Is Part Of: ISRN mathematical physics. Volume 2012(2012)
• Publication Date: 2012-02-12
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Electronic journals; Periodicals; 530.15
• DOI: 10.5402/2012/234516
• Languages: English
• ISSNs: 2090-4673

Abstract

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.