In the Previous Problem, Using the Notation $u _ { i j } = u ( x , \mathrm { t } )$

Multiple Choice

In the previous problem, using the notation $u _ { i j } = u ( x , \mathrm { t } )$ , and letting $\lambda = c k / h$ , the equation becomes

A) $u _ { i , j + 1 } = \lambda ^ { 2 } { } _ { u i } + 1 , j + \left( 1 + 2 \lambda ^ { 2 } \right) u _ { i j } + \lambda _ { u i - 1 , j - u i j - 1 } ^ { 2 }$
B) $u _ { i , j + 1 } = \lambda ^ { 2 } { } _ { u i } + 1 , j + \left( 1 - 2 \lambda ^ { 2 } \right) u _ { i j } + \lambda _ { u i - 1 , j - u i j - 1 } ^ { 2 }$
C) $u _ { i , j + 1 } = \lambda _ { u i + 1 , j } + ( 1 - \lambda ) u _ { i j } + \lambda _ { u i - 1 , j - u i j - 1 }$
D) $u _ { i , j - 1 } = \lambda ^ { 2 } { } _ { u i } + 1 , j + \left( 1 + 2 \lambda ^ { 2 } \right) u _ { i j } + \lambda _ { u i - 1 , j + u i j - 1 } ^ { 2 }$
E) $u _ { i , j - 1 } = \lambda _ { u i + 1 , j } + ( 1 - 2 \lambda ) u _ { i j } + \lambda _ { u i - 1 , j + u i j - 1 }$