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.