Fourth-order approximations at first time level, linear stability analysis and the numerical solution of multidimensional second-order nonlinear hyperbolic equations in polar coordinates

✍ Scribed by R.K. Mohanty; M.K. Jain; Kochurani George

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 546 KB
• Volume: 93
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(98)00054-5

✦ Synopsis

In this article, three-level implicit difference schemes of O(k4+ k2h2+ h 4) where k>0, h>0 are grid sizes in time and space coordinates, respectively, are proposed for the numerical solution of one, two and three space-dimensional nonlinear wave equations in polar coordinates subject to appropriate initial and Dirichlet boundary conditions. We also discuss fourth-order approximation at first time level for more general case. We also obtain the stability range of the difference scheme when applied to a test equation: Gt u,=urr+rU,.--~u+g(r,t), ct=l and 2.

Numerical examples are provided to demonstrate the required order of convergence of the methods.