【摘要】 在再生核空间中讨论了如何求解一类时滞抛物型偏微分方程初边值问题(1.1)。首先利用将两个再生核空间粘在一起的技巧,将延迟项变为有界线性算子,随后利用再生核的技巧,给出了(1.1)精确解的级数形式的表达式,截断即得近似解,误差在范数意义下单调下降。最后的算例说明了算法的有效性。更多还原

【Abstract】 It is discussed on how to solve the initial boundary problem of a class of delay parabolic partial differential equation in reproducing kernel spaces. Firstly, by linking two reproducing kernel spaces together, the delay item is turned into a bounded linear operator. Subsequently, using the technique of reproducing kernel, the exact solution of the considered equation, denoted by series, is given. Truncating the series, the approximate solution is obtained. When increasing the number of the nodes, the error of the approximate solution is decrease monotone in the sense of the norm. The final example shows the efficiency of the proposed method.更多还原