Applying Cubic B-Spline Quasi-Interpolation to Solve 1D Wave Equations in Polar Coordinates. (7th December 2013) - Aminikhah, Hossein; Alavi, Javad
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.