The Improved Euler's Formula for Solving $y ^ { \prime } = f ( x , y ) , y ( \bar { x } ) = \bar { y }$

question 16

Multiple Choice

The improved Euler's formula for solving $y ^ { \prime } = f ( x , y ) , y ( \bar { x } ) = \bar { y }$ is

• A) \(y _ { n + 1 } = y _ { n } - f \left( x _ { n } , y _ { n } \right) , y _ { 0 } = \bar { y } , n = 0,1,2 , \ldots\)
• B) \(y _ { n + 1 } = y _ { n } - h f \left( x _ { n } , y _ { n } \right) , y _ { 0 } = \bar { y } , n = 0,1,2 , \ldots\)
• C) \(y _ { n + 1 } = y _ { n } + h f \left( x _ { n } , y _ { n } \right) , y _ { 0 } = \bar { y } , n = 0,1,2 , \ldots\)
• D) \(y _ { n + 1 } = y _ { n } + \left( f \left( x _ { n } , y _ { n } \right) + f \left( x _ { n + 1 } , y _ { n + 1 } ^ { * } \right) / 2 \right) , y _ { 0 } = \bar { y } , n = 0,1,2 , \ldots \text { where } y _ { n + 1 } ^ { * }\)
• is predicted from Euler's formula
• E) \(y _ { n + 1 } = y _ { n } + h \left( f \left( x _ { n } , y _ { n } \right) + f \left( x _ { n + 1 } , y _ { n + 1 } ^ { * } \right) / 2 \right) , y _ { 0 } = \bar { y } , n = 0,1,2 , \ldots \text { where } y _ { n + 1 } ^ { * }\)
• is predicted from Euler's formula

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