【摘要】 利用有限差分法,构造一个求解一阶线性双曲型偏微分方程组的高精度隐式差分格式.该格式的相容性和收敛性被证明.进一步,Fourier级数法分析表明该格式无条件稳定.另外,该隐式差分格式可以转化为显格式求解,较同类格式的计算量小.通过实例验证,该格式数值结果绘制的图形稳定、光滑、效果良好.更多还原

【Abstract】 In this paper,by the finite difference method,an implicit difference scheme with high accuracy is set up to solve the first order linear hyperbolic partial differential equations. The compatibility and convergence of the scheme are proved. Furthermore,the Fourier series method shows that the difference scheme is unconditionally stable. In addition,in contrast to the homogeneous difference scheme,our implicit difference scheme can be transformed into an explicit one to reduce the quantity of the calculation efficiently. An example is given to show that the graphs produced by numerical results are stable and smooth.更多还原