【摘要】 本文讨论了在分布控制中出现的一类半线性抛物方程的有限差分方法.构造了一个线性化隐式差分格式.证明了差分格式解的存在唯一性、收敛性和无条件稳定性.并给出了L2和L∞范数意义下的收敛阶数为O(h2+τ2).数值例子验证了理论分析结果.更多还原

【Abstract】 In this paper,a linearized finite differnce scheme is designed for semilinear parabolic equations regarding the distributed control.The existence and uniqueness of the difference solution is proved.We also proved convergence and stability of solution of the difference scheme in norm L2 and L∞.The order of accurary of difference scheme is O(h2+τ2).更多还原