The Most Popular Fourth Order Runge-Kutta Method for the Solution $y ^ { t } = f ( x , y ) , y \left( x _ { 0 } \right) = y _ { 0 }$

question 19

Multiple Choice

The most popular fourth order Runge-Kutta method for the solution of $y ^ { t } = f ( x , y ) , y \left( x _ { 0 } \right) = y _ { 0 }$ is

• A) \(\begin{array} { l }
• y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + 2 k _ { 2 } + 2 k _ { 3 } + k _ { 4 } \right) / 6 , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , \\
• k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } / 2 \right) , k _ { 3 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 2 } / 2 \right) , \\
• k _ { 4 } = f \left( x _ { n } + h , y _ { n } + h k _ { 3 } \right)
• \end{array}\)
• B) \(\begin{array} { l }
• y _ { n + 1 } = y _ { n } + h \left( 2 k _ { 1 } + k _ { 2 } + k _ { 3 } + 2 k _ { 4 } \right) / 6 , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , \\
• k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } \right) , k _ { 3 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 2 } \right) , \\
• k _ { 4 } = f \left( x _ { n } + h , y _ { n } + h k _ { 3 } \right)
• \end{array}\)
• C) \(\begin{array} { l }
• y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + 2 k _ { 2 } + 2 k _ { 3 } + k _ { 4 } \right) / 6 , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , \\
• k _ { 2 } = f \left( x _ { n } + h / 3 , y _ { n } + h k _ { 1 } / 2 \right) , k _ { 3 } = f \left( x _ { n } + 2 h / 3 , y _ { n } + h k _ { 2 } / 2 \right) , \\
• k _ { 4 } = f \left( x _ { n } + h , y _ { n } + h k _ { 3 } \right)
• \end{array}\)
• D) \(\begin{array} { l }
• y _ { n + 1 } = y _ { n } + h \left( 2 k _ { 1 } + 2 k _ { 2 } + 2 k _ { 3 } + 2 k _ { 4 } \right) / 6 , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , \\
• k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } / 2 \right) , k _ { 3 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 2 } / 2 \right) , \\
• k _ { 4 } = f \left( x _ { n } + h , y _ { n } + h k _ { 3 } \right)
• \end{array}\)
• E) \(\begin{array} { l }
• y _ { n + 1 } = y _ { n } + h \left( k _ { 1 } + 2 k _ { 2 } + 2 k _ { 3 } + k _ { 4 } \right) / 6 , \text { where } k _ { 1 } = f \left( x _ { n } , y _ { n } \right) , \\
• k _ { 2 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 1 } \right) , k _ { 3 } = f \left( x _ { n } + h / 2 , y _ { n } + h k _ { 2 } \right) , \\
• k _ { 4 } = f \left( x _ { n } + h , y _ { n } + h k _ { 3 } \right)
• \end{array}\)

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Definitions:

Goods A

Indicating a generic category of tangible products or commodities.

Budget Constraint

The financial limit on the consumption choices of an individual or household based on income and the prices of goods and services.

Income Change

A variation in the amount of earnings received by a person, household, or economic entity over a period.

Inferior Good

A good for which an increase in income reduces the quantity demanded