1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
luda_lava [24]
3 years ago
10

Use Euler's method with each of the following step sizes to estimate the value of y(0.4), where y is the solution of the initial

-value problem y' = y, y(0) = 9.(i) h = 0.4 (ii) h = 0.2(iii) h = 0.1
Mathematics
1 answer:
sergey [27]3 years ago
6 0

Answer:

h=0.4--> 15

h=0.2 --> 14.06

h=0.1 --> 13.71

Step-by-step explanation:

This is a numerical solution using Euler's method. Euler's method enables us to numerically approch a solution with a suitable  step size. As the step size gets smaller, the approximation will be more accurate. Euler's method is as the following.

y_{i+1}=y_{i}+h*y_{first derivation}

Here, h is the step size. The reason why first derivation used here is to make an appriximation with using the rate of increase or decrease. As the step size is smaller, the icreases or decreases are followed more accurately. Now, let's solve the question:

for h= 0.4:

y(0.4)=y(0)+0.4*y'

The trick here is y' is equal to y, thus we can write that y'=y(0.4) and our starting point y(0) is given as 9 in the question and the equation becomes:

y(0.4)=9+0.4*y(0.4) and this is easy to solve.By replacing y(0.4) functions to be at the same side of the equation, we get:

0.6*y(0.4)=9 and by solving this equation, y(0.4) is found to be 15.

for h=0.2:

This will be similar to the previous question, but since the step size is 0.2, we will first calculate y(0.2) and then y(0.4).

y(0.2)=y(0)+0.2*y(0.2) and y(0) is 9.

0.8*y(0.2)=9 and y(0.2)=11.25. Now, we will replace this value into the next iteration o the formula istead of y(0). The equation is like:

y(0.4)=y(0.2)+0.2*y(0.4) and y(0.4) is found to be 14.06.

for h=0.1:

This is also similar to the above solutions but will be longer and have 4 iterations.

first iteration: y(0.1)=9+0.1*y(0.1) --> y(0.1)=10

second iteration: y(0.2)=y(0.1)+0.1*y(0.2) --> y(0.2)=11.11

third iteration: y(0.3)=y(0.2)+0.1*y(0.3) --> y(0.3)=12.34

fourth iteration: y(0.4)=y(0.3)+0.1*y(0.4) --> y(0.4)=13.71

As the step size gets smaller, the answer also gets smaller and more accurate. With even smaller step sizes, there will be a better approximation. However, in case you have more complex equations or smaller step sizes, it is recommended to use a computer software to make an approximation.

You might be interested in
Kiana is saving for a new computer that cost $499. So far, she has earned 68 percent of the cost of the computer. How much more
marysya [2.9K]

Answer:

159.68

Step-by-step explanation:

68% of 499 is 339.32

499 -339.32=159.68

hope this helps

6 0
3 years ago
Which is greater 82\8 or 37\4.How do you know.extra answer 50 pt
ozzi
Divide both. 82/8=10.25 37/4=9.25 The first is greater.
4 0
3 years ago
Which is bigger 20% of 400 or 1//4 f 360
nekit [7.7K]
20% =20/100=2/10
20% of 400 =(2/10)*400 =80
1/4 of 360= (1/4)*360 =90
90>80, so 1/4 of 360 is bigger than 20% of 400
7 0
3 years ago
Read 2 more answers
-1/2(2x-6)+9=-8 answer
Oxana [17]

Answer:

x= 20 i think sorry if it's wrong⊙﹏⊙

5 0
3 years ago
Read 2 more answers
Seven students took a quiz. Four of these students received a score above 85 percent. Students who received at least an 85 perce
AfilCa [17]
Four of the 7 students got a sticker, so you need to turn that into a percent. To do that, divide 7 by 4, which gives you .57. That means that 57% of students got a sticker.
5 0
3 years ago
Other questions:
  • Determine whether each pair of lines are parallel, perpendicular, or neither. line n: y = -2x-4 line m: y = -2x+8
    6·1 answer
  • Which circle with center U shows a central angle whose intercepted arc, zv, measures 58 ?
    13·1 answer
  • What is 10 times as much as 0.08?
    8·1 answer
  • In verbal expression
    15·1 answer
  • Hey guys, i have a really big problem with solving these types of questions. Could you tell me how to solve this? Brainliest!
    5·1 answer
  • Rewrite the equation in standard form by expanding it. <br> y= 3 (x+2)^2 - 4
    11·1 answer
  • What is the area of the square base?
    6·2 answers
  • Can someone please answer ASAP!
    9·2 answers
  • Please help immediately! also don't use a link to a website​
    11·1 answer
  • Charlie is trying to cover the shape shown with paper. He will NOT be covering the top and the bottom. How much paper will he ne
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!