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首页> 外文期刊>International Journal of Heat and Mass Transfer >A highly accurate LGSM for severely ill-posed BHCP under a large noise on the final time data
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A highly accurate LGSM for severely ill-posed BHCP under a large noise on the final time data

机译：在最终时间数据上存在较大噪声的情况下，用于严重不适的BHCP的高精度LGSM

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摘要

We consider a backward heat conduction problem (BHCP) in a slab, by subjecting to data at a final time, and some different type boundary conditions at two ends of the slab. The BHCP is known to be highly ill-posed. In order to numerically solve the BHCP we develop a new Lie-group shooting method (LGSM) in the spatial direction. It can retrieve very well the initial data with a high order accuracy. Several numerical examples of the BHCP demonstrate that the LCSM is applicable, even for those of strongly ill-posed ones with a large value of final time. Under the noisy final data the LCSM is robust against the disturbance. The new method is applicable for a severely ill-posed case with a final data very small in the order of 10~(-43), and the noise level is in the order of 10~(-1), of which the numerical solution still has an accuracy in the order of 10~(-2). The results are rather significant in the computations of BHCP.
机译：通过对最后时刻的数据以及在板坯两端的一些不同类型的边界条件进行处理，我们考虑了板坯中的向后导热问题（BHCP）。众所周知，BHCP病情严重。为了从数值上解决BHCP，我们在空间方向上开发了一种新的李群射击方法（LGSM）。它可以很好地检索具有高阶精度的初始数据。 BHCP的几个数值示例证明了LCSM是适用的，即使对于那些病态严重且最终时间值较大的LCSM也是如此。在嘈杂的最终数据下，LCSM能够抵抗干扰。新方法适用于病态严重的情况，最终数据非常小，约为10〜（-43），噪声水平约为10〜（-1），其数值解仍具有约10〜（-2）的精度。结果在BHCP的计算中相当重要。

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