Locally implicit finite element method is a satisfactory numerical method to solve non-linear partial differential equations for its unconditional stability and its high rate of convergence.

认为局部隐式有限元法是一种绝对稳定的方法，且具有快速收敛的性质，是求解非线性偏微分方程的一种有效的数值算法。

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Based on theory of hyperbolic linear partial differential operator, the initial value problem of a kind of quasi-linear hyperbolic equations with non-zero initial values was introduced and studied.

基于双曲型线性偏微分算子理论，引入并研究了具有非零初始值的拟线性双曲型方程的定解问题。

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