numerical methods

Question 1

Change of sign method

Answer 1

Showing it crosses the x axis

Question 2

Problems with the change in sign method

Answer 2

Question 3

Decimal search

Answer 3

increasing by a set interval until there is a change in sign

Question 4

interval bisection

Answer 4

Question 5

no idea

Answer 5

Question 6

• X=g(x) method

Answer 6

 Change equation into recurrence relation

Question 7

how to do x=g(x)

Answer 7

Question 8

failures of x = g(x) method

Answer 8

Question 9

Staircase / cobweb diagram

Answer 9

 Start with CURVE then line

Question 10

when will it converge

Answer 10

 Converge at the root where the gradient of the curve is less than the gradient of the line
 The gradient of the curve is between 0 and 1 – IT WILL CONVERGE

Question 11

when will it be a cobweb + when a staircase

Answer 11

 NEGATIVE CURVE GRADIENT – COBWEB

 POSITIVE – STAIRCASE

Question 12

proof of newton raphson

Answer 12

Question 13

newton raphson

Answer 13

Question 14

failures of newton raphson

Answer 14

Question 15

numerical integration rectangles

Answer 15

more rectangles - more accurate

Question 16

Trapezium rule

Answer 16

Question 17

trapezium rule rule

Answer 17

Always one more ordinate than there is strip

Question 18

underestimate or overestimate

Answer 18

Concave up – overestimate

Concave down – underestimate