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.

To solve the ordinary differential equation

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

Given

and using a step size of , the value of using Runge-Kutta 2^nd order Heun’s method is most nearly

-4297.4

-4936.7

-0.21336
-0.24489

Given

, and using a step size of , the best estimate of Runge-Kutta 2nd order Midpoint method most nearly is

-2.2473
-2.2543
-2.6188
-3.2045

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

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

3904.9 m

3939.7 m

6556.3 m

39397 m

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

, would be

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

Multiple choice questions on other topics

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468 and 0717624. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.