A Fictitious Time Integration Method for One-Dimensional Nonhomogeneous Backward Heat Conduction Problems
Chih-Wen Chang
The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.1, pp. 19-20, 2011, DOI:10.3970/icces.2011.016.019
Abstract In this study, we propose a new numerical approach for solving the nonhomogeneous backward heat conduction problems (BHCPs). A fictitious time I" is used to transform the dependent variable u(x, t) into a new one by (1+I")u(x, t)=: v(x, t, I"), such that the original nonhomogeneous heat conduction equation is written as a new parabolic type partial differential equation in the space of (x, t, I"). Besides, a fictitious viscous damping coefficient can be employed to strengthen the stability of numerical integration of the discretized equations by utilizing a group preserving scheme. Several numerical instances More >