The Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems
نویسندگان
چکیده
The Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems Chih-Wen Chang1, Chein-Shan Liu2 and Jiang-Ren Chang1 Summary By using a quasi-boundary regularization we can formulate 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) we can seek the missing initial conditions through a minimum discrepancy of the target in terms of the weighting factor r ∈ (0, 1). A numerical example is worked out to persuade that this novel approach has good efficiency and accuracy. keywords: Backward heat conduction problem, Lie-group shooting method, Strongly ill-posed problem, Quasi-boundary regularization, Two-point boundary value problem
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