Deck 9: Numerical Solutions of Ordinary Differential Equations

Question 1

When entering the number into a three digit base ten calculator, the round-off error is

A) 0.00143
B) 0.000143
C)
D)
E)

Answer 1

E

Question 2

In the previous problem, the local truncation error in is

A)
B)
C)
D)
E) unknown

Answer 2

A

Question 3

The improved Euler's method is what type of Runge-Kutta method?

A) first order
B) second order
C) third order
D) fourth order
E) It is not a Runge-Kutta method

Answer 3

B

Question 4

The most popular fourth order Runge-Kutta method for the solution of is

A)
B)
C)
D)
E)

Question 5

The local truncation error for the improved Euler's method is

A)
B)
C)
D)
E) unknown

Question 6

The standard central difference approximation of is

A)
B)
C)
D)
E)

Question 7

Using the Adams-Bashforth-Moulton method from the previous three problems, the solution of for with is

A) 1.5003
B) 1.4978
C) 1.4919
D) 1.4967
E) none of the above

Question 8

Using the Adams-Bashforth method from the previous problem, and using the values the solution for with is

A) 1.4978
B) 1.5003
C) 1.4919
D) 1.4967
E) none of the above

Question 9

Using the value of from the previous problem, the Adams-Moulton corrector value for the solution of is

A)
B)
C)
D)
E) none of the above

Question 10

The Euler's method solution for of using is

A) 0.14
B) 0.2
C) 0.21
D) 0.11
E) 0.12

Question 11

The Adams-Bashforth formula for finding the solution of is

A)
B)
C)
D)
E) none of the above

Question 12

Which of the following are second order Runge-Kutta methods for the solution of ? Select all that apply.

A)
B)
C)
D)
E)

Question 13

The improved Euler's formula for solving is

A)
B)
C)
D)
E)

Question 14

The standard backward difference approximation of is

A)
B)
C)
D)
E)

Question 15

The solution of , using the improved Euler's method with is

A) 1.2055
B) 1.21625
C) 1.24205
D) 1.226525
E) 1.235625

Question 16

The solution of , using Euler's method with is

A) 1.01
B) 1.11
C) 1.21
D) 1.22
E) 1.23

Question 17

Using the notation from the text, the finite difference equation for solving the boundary value problem is

A)
B)
C)
D)
E)

Question 18

Using the method from the previous problem, the solution of with is

A) 1.222
B) 1.22
C) 1.2213
D) 1.24
E) 1.21

Question 19

Using the method from the previous problem, the solution of with is

A) 1.241
B) 1.242
C) 1.2422
D) 1.2426
E) 1.2428

Question 20

When entering the number into a three digit base ten calculator, the actual value entered is

A)
B)
C)
D)
E)

Question 21

The solution of for , using the Runge-Kutta method of order four, and using , is

A) 0.0909
B) 0.09999
C) 0.09099
D) 0.09899
E) 0.08899

Question 22

Using the method from the previous problem, the solution of with is

A) 1.24
B) 1.241
C) 1.214
D) 1.2214
E) 1.224

Question 23

The Euler formula for solving the system is

A)
B)
C)
D)
E) none of the above

Question 24

A popular second order Runge-Kutta method for the solution of is

A)
B)
C)
D)
E) none of the above

Question 25

The Adams-Bashforth formula for finding the solution of is

A)
B)
C)
D)
E) none of the above

Question 26

Using the method from the previous two problems, using the values the solution of with is

A) 1.4919
B) 1.4967
C) 1.4978
D) 1.5003
E) none of the above

Question 27

The solution of , using the improved Euler's method with is

A) 1.22125
B) 1.210625
C) 1.226525
D) 1.21525
E) 1.221025

Question 28

When entering the number into a three digit base ten calculator, the actual value entered is

A)
B)
C)
D)
E)

Question 29

The fourth order Runge-Kutta method for solving is

A)
B)
C)
D)
E)

Question 30

The problem can be written as a system of two equations as follows.

A)
B)
C)
D)
E)

Question 31

Using the value of from the previous problem, the Adams-Moulton corrector value for the solution of is

A)
B)
C)
D)
E) none of the above

Question 32

In the previous problem, the local truncation error in is

A)
B)
C)
D)
E) unknown

Question 33

Euler's formula for solving is

A)
B)
C)
D)
E)

Question 34

When entering the number into a three digit base ten calculator, the round-off error is

A)
B)
C)
D)
E)

Question 35

Euler's method is what type of Runge-Kutta method?

A) first order
B) second order
C) third order
D) fourth order
E) It is not a Runge-Kutta method

Question 36

The most popular fourth order Runge-Kutta method for the solution of is

A)
B)
C)
D)
E)

Question 37

The solution of , using Euler's method with is

A) 1.01
B) 1.1
C) 1.11
D) 1.21
E) 1.22

Question 38

Using the method from the previous problem, the solution of with is

A) 1.2
B) 1.21
C) 1.214
D) 1.22
E) 1.24

Question 39

Using Euler's method on the previous problem and using a value of , the solution for is

A) 0.11
B) 0.2
C) 0.21
D) 0.22
E) 0.221

Question 40

The local truncation error for the improved Euler's method is

A) unknown
B)
C)
D)
E)