1)Select all that applies to the Fourth-order Runge-Kutta (RK4)method K subscript

1 equals f left parenthesis t subscript k comma y subscript kright parenthesis K subscript

2 equals f left parenthesis t subscript k plus h over 2 commaspace y subscript k plus h over 2 space K subscript 1 rightparenthesis K subscript

3 equals f left parenthesis t subscript k plus h over 2 commaspace y subscript k plus h over 2 space K subscript 2 rightparenthesis K subscript

4 equals f left parenthesis t subscript k plus h comma space ysubscript k plus h space K subscript 3 right parenthesis

2) y subscript k plus 1 end subscript equals ? Select one ormore:

A. - It has four function evaluations - and y subscript k plus 1end subscript equals y subscript k plus space left parenthesis 1third space K subscript 1 plus 2 over 3 space K subscript 2 plus 2over 3 space K subscript 3 plus 1 third space K subscript 4 rightparenthesis space h over 2

B. - It is a fourth-order accurate method - and it has sevenfunction evaluations

C. All of the above.

D. K subscript 1 comma space K subscript 2 comma space Ksubscript 3 space a n d space K subscript 4 are also called slopesof the solution curve or integral curve.

E. The method is named after two German Mathematicians Runge andKutta.