【摘要】 对于二阶双曲型偏微分方程初边值问题,可以用有限差分法进行求解。通常的有限差分法在使用过程中受到精确度和稳定性的限制,本文提出求解二阶双曲型方程的精细时程积分法。由于这种方法是半解析方法,在时间域上可以精确计算,所以这种方法不仅精确度高,而且还绝对稳定。文末的数值算例进一步验证了上述结论,而且对大的时间步长(例如Δt=0.5)仍然获得精度很高的数值结果。可见,精细时程积分法是一种很实用的方法。更多还原

【Abstract】 The initial boundary value problem of the second order hyperbolic partial differential equations can be solved by using finite difference method.However, the usual finite difference method faces the problems of numerical stability and precision, the precise time\|integration method is proposed for the second order hyperbolic differential equations in this paper.The method is a semi\|analytical method, hence it can be accurately solved on time domain and it has accurate and absolutely stable.The numerical example shows that the method has high accuracy even for very large time\|step sizes(e.g.Δt=0.5) and good practicability.更多还原