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

question 40

Multiple Choice

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

---

Definitions:

Marginal Utility

The additional satisfaction or utility that a consumer derives from consuming an additional unit of a good or service.

Purchases

The act of buying goods or services.

Product X

A placeholder name used to refer to a generic or unspecified product in economic and marketing contexts.

Rational Consumer

The theoretical concept of a consumer who always makes decisions that provide the greatest benefit or utility according to their preferences.