Past Cone Dynamics and Backward Group Preserving Schemes for Backward Heat Conduction Problems
C.-S. Liu1, C.-W. Chang2, J.-R. Chang2
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 67-82, 2006, DOI:10.3970/cmes.2006.012.067
Abstract In this paper we are concerned with the backward problems governed by differential equations. It is a first time that we can construct a backward time dynamics on the past cone, such that an augmented dynamical system of the Lie type X˙ = B(X,t)X with t ∈ R−, X ∈ Mn+1 lying on the past cone and B ∈ so(n,1), was derived for the backward differential equations system x· =f(x,t), t ∈ R−, x ∈ Rn. These two differential equations systems are mathematically equivalent. Then we apply the backward group preserving scheme (BGPS), which is an explicit single-step algorithm… More >
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