The five point approximation of the Laplacian is
A) $[ u ( x + h , y ) + u ( x , y + h ) + u ( x - h , y ) + u ( x , y - h ) - 2 u ( x , y ) ] / h$
B) $[ u ( x + h , y ) + u ( x , y + h ) + u ( x - h , y ) + u ( x , y - h ) - 4 u ( x , y ) ] / h$
C) $[ u ( x + h , y ) + u ( x , y + h ) + u ( x - h , y ) + u ( x , y - h ) - 2 u ( x , y ) ] / h ^ { 2 }$
D) $[ u ( x + h , y ) + u ( x , y + h ) + u ( x - h , y ) + u ( x , y - h ) - 4 u ( x , y ) ] / h ^ { 2 }$
E) $[ u ( x + h , y ) - u ( x , y + h ) + u ( x - h , y ) - u ( x , y - h ) - 4 u ( x , y ) ] / h ^ { 2 }$

Question

Quizplus · Accepted Answer

The five-point approximation of the Laplacian uses values at a point, its immediate neighbors to the left, right, above, and below, and subtracts four times the value at the point itself, all divided by $h^2$, to approximate the second derivatives in both x and y directions.

The Five Point Approximation of the Laplacian Is A) [u(x+h,y)+u(x,y+h)+u(x−h,y)+u(x,y−h)−2u(x,y)]/h[ u ( x + h , y ) + u ( x , y + h ) + u ( x - h , y ) + u ( x , y - h ) - 2 u ( x , y ) ] / h[u(x+h,y)+u(x,y+h)+u(x−h,y)+u(x,y−h)−2u(x,y)]/h

The Five Point Approximation of the Laplacian Is
A) $[ u ( x + h , y ) + u ( x , y + h ) + u ( x - h , y ) + u ( x , y - h ) - 2 u ( x , y ) ] / h$