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In this paper, the convergence and stability of Galerkin finite element method for a hyperbolic partial differential equations with piecewise continuous arguments are investigated. Firstly, the variation formulation is derived by applying Green's formula and Galerkin finite element method to spatial direction of the original equation. Next, semidiscrete and fully discrete schemes are obtained and the convergence is analyzed in L 2 -norm rigorously. Moreover, the stability analysis shows that the semidiscrete scheme can achieve unconditionally stability. The sufficient conditions of stability for fully discrete scheme are also obtained under which the analytic solution is asymptotically stable. Finally, some numerical experiments are provided to demonstrate our theoretical results.

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The construction of a perfect evaluation index system of professional literacy of pre-science teachers is the basis of measuring the level of professional literacy of pre-science teachers in Xinjiang. It is of great practical significance to identify the advantages and disadvantages of education of pre-science teachers in Xinjiang. Based on “Professional Standards” and “Certification Standards”, this paper constructs an evaluation index system of Xinjiang pre-science teachers’ professional literacy, including 3 first-level indicators and 18 second-level indicators.