一维线性抛物型方程边界值反演的TBG方法

TBG Method for the Inversion of Boundary Value Relation to One-Dimensional Linear Parabolic Equations

提出了一种新的数值反演一维线性抛物型方程边界值的ＴＢＧ方法，它是将一般的一维线性抛物型方程边界值反问题转化为等价的第一类Ｆｒｅｄｈｏｌｍ积分方程，给出了该方法近似解的收敛性证明和渐近阶的估计。该方法不仅可以孤立的求得解在某一点ξ的值，而且便于推广到ｎ维线性抛物型方程边界值反演的情形。

A new numerical method-TBG method for the inversion of boundary value relation to one-dimensional linear parabolic equations is proposed. The convergence of approximate solution and the estimation of asymptolic order are discussed. The method is not only able to slove the value of certain point ξ in the solution alone, but also easy to extend the case of the inversion of boundary value for n -dimensional parabolic equations.