Numerical Methods

Question 1

What are the possible roots from this graph?

Answer 1

x = -8

x = 12

x = 26

Question 2

What is the formula for the Jacobi Method?

Answer 2

Question 3

A function is tabulated at points…(eqn)

Answer 3

…where r = …, -1, 0, 1, 2… and h is the fized interval of tabulation

Question 4

The forward difference operator ∆ is defined as…(eqn)

Answer 4

Question 5

For the forward difference operator, the second difference is formed from computing the…(defintion and equation)

Answer 5

…difference between two differences

Question 6

What is the Newton Gregory Formula? (eqn)

The value of the function f(x) when x = x₀ + ph can be written as…

Answer 6

Question 7

p

n

= ?

Answer 7

Question 8

How many forward differences can be calculated from this table?

Answer 8

With only six data points, only five forward differences can be calculated

Question 9

What would the forward difference table of this look like?

Answer 9

Question 10

Which rule is more accurate? Simpsons or trapezium?

Answer 10

Simpsons rule

Question 11

What is the difference between the trapezium rule and the composite trapezium rule?

Answer 11

The composite trapezium rule takes smaller intervals

Question 12

What are the equations and graph for Euler’s method?

Answer 12

Question 13

What are the equations and graph for the second order Runge-Kutta method? (Slightly different to the formula book)

Answer 13

Question 14

What is the formula for the fourth-order Runge-Kutta method? (In formula book)

Answer 14

Question 15

Which is the most accurate out of, Euler method, second order Runge-Kutta, and fourth order Runge-Kutta?

Answer 15