【摘要】 本文构造了一类求解非线性时滞双曲型偏微分方程的紧致差分格式,获得了该差分格式的唯一可解性,收敛性和无条件稳定性,收敛阶为O(Γ~2+h~4),并进一步对时间方向进行Richardson外推,使得收敛阶达到了O(Γ~4+h~4).数值实验表明了算法的精度和有效性.更多还原

【Abstract】 In this paper,a class of compact difference schemes are constructed to solve the nonlinear delay hyperbolic partial differential equations.The unique solvability,convergence and unconditional stability of the scheme are obtained.The convergence order is O(r~2+h~4).Furthermore,the Richardson extrapolation is applied to improve the temporal accuracy of the scheme,and a solution of order four in both temporal and spatial dimensions is obtained.Numerical example shows the accuracy and efficiency of the algorithms.更多还原