Finite-difference methods have come into wide use for solving special problems including transient-heat conduction. Dusinberre has ably presented the possibilities of finite-difference methods. The success of most such methods depends on the existence of a certain degree of uniformity of behavior of the temperature over the finite intervals of both space and time selected for the computation process. In some cases, however, this required uniformity constitutes a handicap since temperatures are changing so rapidly that inconveniently short time intervals have to be chosen. This paper represents an effort to develop a finite-difference method free from the foregoing defect.

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