A popular second order Runge-Kutta method for the solution of $y ^ { t } = f ( x , y ) , y \left( x _ { 0 } \right) = y _ { 0 }$ is
A) $\begin{array} { l }
y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) \
k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } / 2 \right)
\end{array}$
B) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h , y _ { n } + h k _ { 1 } / 2 \right)$
C) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } \right)$
D) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h , y _ { n } + h k _ { 1 } \right)$
E) none of the above

Question

A popular second order Runge-Kutta method for the solution of $y ^ { t } = f ( x , y ) , y \left( x _ { 0 } \right) = y _ { 0 }$ is
A) $\begin{array} { l } 
y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) \
k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } / 2 \right)
\end{array}$
B) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h , y _ { n } + h k _ { 1 } / 2 \right)$
C) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } \right)$
D) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h , y _ { n } + h k _ { 1 } \right)$
E) none of the above

Quizplus · Accepted Answer

The Answer of A popular second order Runge-Kutta method for the solution of $y ^ { t } = f ( x , y ) , y \left( x _ { 0 } \right) = y _ { 0 }$ is
A) $\begin{array} { l } 
y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) \
k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } / 2 \right)
\end{array}$
B) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h , y _ { n } + h k _ { 1 } / 2 \right)$
C) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } \right)$
D) $y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h , y _ { n } + h k _ { 1 } \right)$
E) none of the above

A Popular Second Order Runge-Kutta Method for the Solution Of y