Applying Cubic B-Spline Quasi-Interpolation to Solve 1D Wave Equations in Polar Coordinates. (7th December 2013)

• Record Type: Journal Article
• Authors: Aminikhah, Hossein; Alavi, Javad
• Other Names: Peng Y. Academic Editor.; Zhou J. G. Academic Editor.
• Is Part Of: ISRN computational mathematics. Volume 2013(2013)
• Publication Date: 2013-12-07
• Subjects: Numerical analysis -- Periodicals; Mathematics -- Data processing -- Periodicals; Mathematics -- Data processing; Numerical analysis; Electronic journals; Periodicals; 510
• DOI: 10.1155/2013/710529
• Languages: English
• ISSNs: 2090-7842

Abstract

Abstract : We provide numerical solution to the one-dimensional wave equations in polar coordinates, based on the cubic B-spline quasi-interpolation. The numerical scheme is obtained by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a forward difference to approximate the time derivative of the dependent variable. The accuracy of the proposed method is demonstrated by three test problems. The results of numerical experiments are compared with analytical solutions by calculating errors L 2 -norm and L ∞ -norm. The numerical results are found to be in good agreement with the exact solutions. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement.