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On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients. (English) Zbl 0877.65066
Three level-implicit difference schemes of order 4 are developed for initial-boundary value problems for a linear system of wave equations with variable coefficients and nonlinear lower-order terms. The difference scheme is particularly adapted for the singular lower-order term arising at the origin when solving the scalar wave equations in cylindrical and spherical symmetry. A linear stability analysis is performed. The convergence order is verified on numerical examples.

MSC:
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35L70Nonlinear second-order hyperbolic equations
35L05Wave equation (hyperbolic PDE)