Chen, P.Y.P. (2014) Axisymmetric Thermal Stresses in an Anisotropic Finite Hollow Cylinder. In: Hetnarski, R.B., Ed., Encyclopedia of Thermal Stresses, Springer, Dordrecht, 295-304.
https://www.springer.com/gp/book/9789400727380
https://doi.org/10.1007/978-94-007-2739-7_210

has been cited by the following article:

• TITLE: On Transient Simulation of Field Equations

  AUTHORS: Peter Chen

  KEYWORDS: Solution of Differential Equations, Transient Simulation, Numerical Instability, Mathematical Modelling, Backward Time Integration

  JOURNAL NAME: Applied Mathematics, Vol.10 No.9, September 9, 2019

  ABSTRACT: We investigate under what conditions transient simulation could be used to integrate backward in time so that the initial field could be recovered from later histories. In this paper we use realistic examples and find that, in long histories, traces of the initial field would be present only in the exact analytical solutions. We conclude that the recovery of initial field is possible only if the equations could be solved analytically or only short time periods are involved. In practice, it is not possible to detect those traces by measurements or observations. If numerical procedures are used, truncation and discretization errors are always present. Fine-tuning of system parameters used or transforming time into another pseudo time frame may allow numerical integration to be carried out backward in time. But numerical instability is still a problem. Large spurious increases found by numerical procedures are most likely due to numerical inaccuracy and instability.