Studies on the Method of Orthogonal Collocation: I-A One-Point Collocation Method for the Transient Heat Conduction Problem

A one-point collocation scheme is developed for the transient heat conduction problem. The scheme makes use of the asymptotic solution of the problem for short time and the fact that initially the temperature profile can be divided into two zones, a fast temperature changing zone and inactive zone. For long time a Biot number dependent collocation point is used. The method provides approximate solutions which compares well with the numerical solution and other approximate solutions.