Use Euler's method with step size h = 0.2 to approxi- mate the solution to the initial value problem 1 y' y² = ² = (y² + y)₂ y(1) = 1 X at the points x = 1.2, 1.4, 1.6, and 1.8.
Use Euler's method with step size h = 0.2 to approxi- mate the solution to the initial value problem 1 y' y² = ² = (y² + y)₂ y(1) = 1 X at the points x = 1.2, 1.4, 1.6, and 1.8.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:6. Use Euler's method with step size h
mate the solution to the initial value problem
= 0.2 to approxi-
y' = (y²
0? + y). y(1) = 1
|
at the points x =
1.2, 1.4, 1.6, аnd 1.8.
Transcribed Image Text:8. Use the improved Euler's method subroutine with step
0.2 to approximate the solution to the initial
size h
value problem
y' = {o* +y).
1
y(1) = 1,
at the points x = 1.2, 1.4, 1.6, and 1.8. (Thus,
input N = 4.) Compare these approximations with
those obtained using Euler's method (see Exercises 1.4,
Problem 6, page 28).
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Since you have asked multiple questions, we will solve the first Question for you. If you want any specific question to be solved, then please specify the question number or post only that question.
The given differential equation is with .
The given step size is .
We know that the iteration to solve the differential equation with step size using Euler's method is calculated as:
, where .
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