Which of the Following Are Second Order Runge-Kutta Methods for the Solution

question 11

Multiple Choice

Which of the following are second order Runge-Kutta methods for the solution of $y ^ { t } = f ( x , y ) , y \left( x _ { 0 } \right) = y _ { 0 }$ ? Select all that apply.

• A) \(y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + h , y _ { n } + h k _ { 1 } \right)\)
• B) \(\begin{array} { l }
• y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } / 3 + 2 k _ { 2 } / 3 \right) , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) \\
• k _ { 2 } = f \left( x _ { n } + 3 h / 4 , y _ { n } + 3 h k _ { 1 } / 4 \right)
• \end{array}\)
• C) \(\begin{array} { l }
• y _ { n + 1 } = y _ { n } + h \left( 2 k _ { 1 } / 3 + k _ { 2 } / 3 \right) , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) \\
• k _ { 2 } = f \left( x _ { n } + 3 h / 2 , y _ { n } + 3 h k _ { 1 } / 2 \right)
• \end{array}\)
• D) \(y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + k _ { 2 } \right) / 2 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + 2 h , y _ { n } + 2 h k _ { 1 } \right)\)
• E) \(y _ { n + 1 } = y _ { n } + h \left( 3 k _ { 1 } + k _ { 2 } \right) / 4 \text {, where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , k _ { 2 } = f \left( x _ { n } + 2 h , y _ { n } + 2 h k _ { 1 } \right)\)

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