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

question 37

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

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Definitions:

Mental Repression

A defense mechanism where unpleasant thoughts, memories, or desires are pushed from the conscious mind into the unconscious.

Highly Embarrassing

Highly embarrassing refers to situations or events that cause an intense feeling of shame or discomfort, often due to social faux pas or personal failures.

Psychoanalytic Framework

A theoretical model that emphasizes unconscious psychological processes (such as desires and fears) and early childhood experiences as determinants of behavior and mental disorders.

Transference

Transference is a psychological phenomenon in which an individual unconsciously redirects feelings and attitudes from a person or situation in the past to a person or situation in the present, especially in psychotherapy contexts.