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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.

Reviewer: R.Jeltsch (Zürich)

### MSC:

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

35L70 | Second-order nonlinear hyperbolic equations |

35L05 | Wave equation |

### Keywords:

difference methods; linear wave equation; variable coefficients; cylindrical and spherical symmetry; linear stability analysis; convergence; numerical examples
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\textit{R. K. Mohanty} et al., J. Comput. Appl. Math. 72, No. 2, 421--431 (1996; Zbl 0877.65066)

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### References:

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