High accuracy difference schemes for a class of singular three space dimensional hyperbolic equations

Abstract

For the numerical integration of the system of 3-D nonlinear hyperbolic equations with variable coefficients, we report two three-level implicit difference methods of 0(k ⁴ + k ² h ² + h ⁴) where k and h are grid sizes in time and space directions, respectively. When the coefficients of u_xy, u_yz and u_yzare equal to zero we require only (7+19 + 7) grid points and when the coefficients of u_xy, u_yz and u_zx are not equal to zero and the coefficients of u_xx, u_yy and u_zz are equal we require (19+27+19) grid points. The three-level conditionally stable ADI method of 0 (k4 + k ² h ²+ h ⁴) for the numerical solution of wave equation in polar coordinates is discussed. Numerical examples are provided to illustrate the methods and their fourth order convergence.

Keywords:

• Singular hyperbolic equations
• Finite difference methods
• Nonlinear wave equation
• Root mean square errors
• Maximum absolute errors

^* CSIR Fellowship to one of the authors Kochuraniu George is greatly acknowledeged

^* CSIR Fellowship to one of the authors Kochuraniu George is greatly acknowledeged

Notes

^* CSIR Fellowship to one of the authors Kochuraniu George is greatly acknowledeged