Runge_Kutta 2nd order Method of Ordinary Differential Equations

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MULTIPLE CHOICE TEST (All Tests)	RUNGE-KUTTA 2nd ORDER METHOD (More on Runge-Kutta 2nd Order Method)	ORDINARY DIFFERENTIAL EQUATIONS (More on Ordinary Differential Equations)

Pick the most appropriate answer.

Q1. To solve the ordinary differential equation

by the Runge-Kutta 2^nd order method, you need to rewrite the equation as

Q2. Given

and using a step size of h=0.3, the value of y(0.9) using the Runge-Kutta 2^nd order Heun's method is most nearly

-4297.4

-4936.7

-0.21336
-0.24489

Q3. Given

and using a step size of h=0.3, the best estimate of dy/dx(0.9) using the Runge-Kutta 2nd order midpoint-method most nearly is

-2.2473
-2.2543
-2.6188
-3.2045

Q4. The velocity (m/s) of a body is given as a function of time (seconds) by

Using the Runge-Kutta 2^nd order Ralston method with a step size of 5 seconds, the distance in meters traveled by the body from t=2 to t=12 seconds is estimated most nearly is

3904.9

3939.7

6556.3

39397

Q5. The Runge-Kutta 2^nd order method can be derived by using the first three terms of the Taylor series of writing the value of y_i₊₁ (that is the value of y at x_i₊₁ ) in terms of y_i (that is the value of y at x_i) and all the derivatives of y at x_i . If h=x_i₊₁-x_i, the explicit expression for y_i₊₁ if the first three terms of the Taylor series are chosen for solving the ordinary differential equation