【摘要】 对一类带有Dirichlet边界条件的延迟非线性抛物偏微分方程的初边值问题建立了一个Crank-Nicolson型的线性化差分格式,用离散能量法证明了该差分格式在L_∞范数下是无条件收敛的且是稳定的,其收敛阶为O(r~2+h~2).最后,用数值算例验证了理论结果.更多还原

【Abstract】 A linearized Crank-Nicolson scheme is estabilished for a class of delay nonlinear parabolic differential equations with Dirichlet boundary value conditons.It is proved that the difference scheme is unconditionally stable and convergent in L_∞norm.The convergence order is O(r~2 + h~2).Finally,a numerical exmple is provided to testify the theoretical results.更多还原