(All Tests)


(More on Runge-Kutta 2nd Order Method)


(More on Ordinary Differential Equations)


Pick the most appropriate answer.

Q1. To solve the ordinary differential equation


by the Runge-Kutta 2nd 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 2nd order Heun's method is most nearly




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


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


Using the Runge-Kutta 2nd 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





Q5. The Runge-Kutta 2nd order method can be derived by using the first three terms of the Taylor series of writing the value of yi+1 (that is the value of y at xi+1 ) in terms of yi  (that is the value of y at xi) and all the derivatives of y at xi .  If h=xi+1-xi, the explicit expression for yi+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/(kg-K)

density of ball = 7800

convection coefficient = 350 J/s-m^2-K

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                       





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