MULTIPLE CHOICE TEST 
RUNGEKUTTA 2nd ORDER METHOD 
ORDINARY DIFFERENTIAL EQUATIONS 
Pick the most appropriate answer. 


Q1. To solve the ordinary differential equation
by the RungeKutta 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 RungeKutta 2^{nd} order Heun's method is most nearly 4297.4 4936.7
0.21336 Q3. Given ,
and using a step size of h=0.3, the best estimate of dy/dx(0.9) using the RungeKutta 2nd order midpointmethod most nearly is
2.2473 Q4. The velocity (m/s) of a body is given as a function of time (seconds) by
Using the RungeKutta 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 RungeKutta 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
would be
Q6. A spherical ball is taken out of a furnace at 1200K and is allowed to cool in air. Given the following, radius of ball = 2 cm specific heat of ball = 420 J/(kgK) density of ball = 7800 convection coefficient = 350 J/sm^2K The ordinary differential equation is given for the temperature, of the ball
if only radiation is accounted for. The ordinary differential equation if convection is accounted for in addition to radiation is
