Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q 3.6-12E

Fundamentals Of Differential Equations And Boundary Value Problems
Found in: Page 130
Fundamentals Of Differential Equations And Boundary Value Problems

Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Use the improved Euler’s method with tolerance to approximate the solution to y'=1-siny,y(0)=0, at x=π. For a tolerance of ε=0.01, use a stopping procedure based on the absolute error.

The required result is ϕπ=1.09580

See the step by step solution

Step by Step Solution

Step 1: Important formula.

The required Euler’s formula,


Step 2: Find the equation of approximation value

Here given y'=1-siny,y0=0 ,

For value of ε=0.01 , x = 0, y0 = 0, c=π , M = 10, h = 3.141593 then


Step 3: solve for x and y

Apply initial points



Hence, the value is ϕπ=y1,3.141593=3.14159

Step 4: Evaluate the value of  x and y 

Now, for the values of x=0,y=0,h=1.570796



Step 5: Determine the value of x and t for the conditions

Now, for the values of F and G



The value of ϕπ=y1,0.570796=1.05663

Step 6: Determine the all-other values.

Apply the same procedure for all other values and the values are


Since the value is

role="math" localid="1664308176524" y1,0.196350-y1,0.392699=1.09580-1.09229=0.00351<0.01ϕπ=1.09580

Therefore, the result is ϕπ=1.09580

Most popular questions for Math Textbooks


Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.