کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
662039 | 1458160 | 2007 | 8 صفحه PDF | دانلود رایگان |
A quasi-boundary regularization leads to a two-point boundary value problem of the backward heat conduction equation. The ill-posed problem is analyzed by using the semi-discretization numerical schemes. Then the resulting ordinary differential equations in the discretized space are numerically integrated towards the time direction by the Lie-group shooting method to find the unknown initial conditions. The key point is based on the erection of a one-step Lie group element G(T) and the formation of a generalized mid-point Lie group element G(r ). Then, by imposing G(T)=G(r)G(T)=G(r) we can search for the missing initial conditions through a minimum discrepancy of the targets in terms of the weighting factor r∈(0,1)r∈(0,1). Several numerical examples were worked out to persuade that this novel approach has good efficiency and accuracy. Although the final temperature is almost undetectable and/or is disturbed by large noise, the Lie group shooting method is stable to recover the initial temperature very well.
Journal: International Journal of Heat and Mass Transfer - Volume 50, Issues 11–12, June 2007, Pages 2325–2332