The Adams-Bashforth Formula for Finding the Solution Of $y ^ { t } = f ( x , y ) , y \left( x _ { 0 } \right) = y _ { 0 }$

question 10

Multiple Choice

The Adams-Bashforth formula for finding the solution of $y ^ { t } = f ( x , y ) , y \left( x _ { 0 } \right) = y _ { 0 }$ is

• A) \(\begin{array} { l }
• y _ { n + 1 } ^ { * } = y _ { n } + h \left( 55 y _ { n } ^ { \prime } + 59 y _ { n - 1 } ^ { \prime } - 37 y _ { n - 2 } ^ { \prime } - 9 y _ { n - 3 } ^ { \prime } \right) / 24 , \text { where } y _ { n } ^ { \prime } = f \left( x _ { n } , y _ { n } \right) \\
• y _ { n - 1 } ^ { \prime } = f \left( x _ { n - 1 } , y _ { n - 1 } \right) , y _ { n - 2 } ^ { \prime } = f \left( x _ { n - 2 } , y _ { n - 2 } \right) , y _ { n - 3 } ^ { \prime } = f \left( x _ { n - 3 } , y _ { n - 3 } \right)
• \end{array}\)
• B) \(\begin{array} { l }
• y _ { n + 1 } ^ { * } = y _ { n } + h \left( 55 y _ { n } ^ { \prime } - 59 y _ { n - 1 } ^ { \prime } + 37 y _ { n - 2 } ^ { \prime } - 9 y _ { n - 3 } ^ { \prime } \right) / 24 , \text { where } y _ { n } ^ { \prime } = f \left( x _ { n } , y _ { n } \right) \\
• y _ { n - 1 } ^ { \prime } = f \left( x _ { n - 1 } , y _ { n - 1 } \right) , y _ { n - 2 } ^ { \prime } = f \left( x _ { n - 2 } , y _ { n - 2 } \right) , y _ { n - 3 } ^ { \prime } = f \left( x _ { n - 3 } , y _ { n - 3 } \right)
• \end{array}\)
• C) \(\begin{array} { l }
• y _ { n + 1 } ^ { * } = y _ { n } + h \left( 55 y _ { n } ^ { \prime } - 59 y _ { n - 1 } ^ { \prime } - 37 y _ { n - 2 } ^ { \prime } + 65 y _ { n - 3 } ^ { \prime } \right) / 24 , \text { where } y _ { n } ^ { \prime } = f \left( x _ { n } , y _ { n } \right) \\
• y _ { n - 1 } ^ { \prime } = f \left( x _ { n - 1 } , y _ { n - 1 } \right) , y _ { n - 2 } ^ { \prime } = f \left( x _ { n - 2 } , y _ { n - 2 } \right) , y _ { n - 3 } ^ { \prime } = f \left( x _ { n - 3 } , y _ { n - 3 } \right)
• \end{array}\)
• D) \(\begin{array} { l }
• y _ { n + 1 } ^ { * } = y _ { n } + h \left( 59 y _ { n } ^ { \prime } - 55 y _ { n - 1 } ^ { \prime } + 37 y _ { n - 2 } ^ { \prime } - 17 y _ { n - 3 } ^ { \prime } \right) / 24 , \text { where } y _ { n } ^ { \prime } = f \left( x _ { n } , y _ { n } \right) \\
• y _ { n - 1 } ^ { \prime } = f \left( x _ { n - 1 } , y _ { n - 1 } \right) , y _ { n - 2 } ^ { \prime } = f \left( x _ { n - 2 } , y _ { n - 2 } \right) , y _ { n - 3 } ^ { \prime } = f \left( x _ { n - 3 } , y _ { n - 3 } \right)
• \end{array}\)
• E) none of the above

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