The central difference approximation for $\frac { \partial u } { \partial x }$ with step size $h$ is
A) $( u ( x + h , y ) - 2 u ( x , y ) + u ( x - h , y ) ) / h$
B) $( u ( x + h , y ) - 2 u ( x , y ) + u ( x - h , y ) ) / h ^ { 2 }$
C) $( u ( x , y + h ) - 2 u ( x , y ) + u ( x , y - h ) ) / h$
D) $( u ( x , y + h ) - 2 u ( x , y ) + u ( x , y - h ) ) / h ^ { 2 }$
E) $( u ( x + h , y ) - u ( x - h , y ) ) / ( 2 h )$

Question

Quizplus · Accepted Answer

The central difference approximation for the first derivative $\frac{\partial u}{\partial x}$ with step size $h$ is given by $(u(x+h,y) - u(x-h,y)) / (2h)$, which is a symmetric difference quotient.

The Central Difference Approximation For ∂u∂x\frac { \partial u } { \partial x }∂x∂u​

The Central Difference Approximation For $\frac { \partial u } { \partial x }$