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) $( u ( x + h , y ) - u ( x - h , y ) ) / ( 2 h )$

Question

Quizplus · Accepted Answer

The central difference approximation for the second derivative $\frac{\partial^2 u}{\partial x^2}$ is given by $(u(x+h,y) - 2u(x,y) + u(x-h,y)) / h^2$, which accurately represents the change in $u$ with respect to $x$, squared, considering both the forward and backward steps from $x$.

The Central Difference Approximation For ∂2u∂x2\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }∂x2∂2u​

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