The forward difference approximation of $\frac { \partial u } { \partial t }$ with step size k is
A) $( u ( x + k , t ) - u ( x , t ) ) / k$
B) $( u ( x - k , t ) - u ( x , t ) ) / k ^ { 2 }$
C) $( u ( x , t + k ) - u ( x , t ) ) / k$
D) $( u ( x , t - k ) - u ( x , t ) ) / k$
E) $( u ( x , t + k ) - u ( x , t ) ) / k ^ { 2 }$

Question

Quizplus · Accepted Answer

The forward difference approximation of a derivative is given by the value at a forward point minus the value at the current point, all divided by the step size. Since we are approximating $\frac{\partial u}{\partial t}$, we need the change in $u$ with respect to $t$, not $x$, and thus the correct formula is $(u(x, t+k) - u(x, t)) / k$, which matches choice C.

The Forward Difference Approximation Of ∂u∂t\frac { \partial u } { \partial t }∂t∂u​

The Forward Difference Approximation Of $\frac { \partial u } { \partial t }$