The Central Difference Approximation For $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$

Multiple Choice

The central difference approximation for $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$ 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) $( u ( x + h , y ) - u ( x - h , y ) ) / ( 2 h )$