Show that in the limit ?x ? 0 and ?t ? 0, the difference is equivalent to the differential
GIVEN
The difference equation for one-dimensional transient conduction
SHOW
(a) As ?x and ?t ?0, the difference equation is equivalent to the differential equation,
Equation is,
By definition
So, the difference equation is equivalent to
In the limit as ?t ??0, from calculus, the left hand side of the above equation becomes
and in the limit as ?x ? 0, from calculus, the first term on the right hand side of the equation becomes
So the equation is equivalent to
which is the same
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