Computation 2: use the 4th order Runge-Kutta method to solve the differential equation du = (y-x-1) ²³ +2 to find an approximate solution. _y (0)=1; Find y (1) with h = 0.2. Find %.ET. Exact answer : y tan x + x + 1 = tan 1+1+1 = 3.557401 = 3.56
Computation 2: use the 4th order Runge-Kutta method to solve the differential equation du = (y-x-1) ²³ +2 to find an approximate solution. _y (0)=1; Find y (1) with h = 0.2. Find %.ET. Exact answer : y tan x + x + 1 = tan 1+1+1 = 3.557401 = 3.56
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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![Computation 2:
use the 4th order Runge-Kutta method to solve the differential
(y-x-1)² +2 to find an approximate solution.
dy
equation
_y (0)=1 Find y(1) with h = 0.2. Find %.E.T.
Exact answer :
y = fan x + x + 1 = tan 1 + 1 + 1 = 3.557401 = 3.56
All answer must be correct to 2 decimal places.
|xn|yn|m₁ = h [f(xn₁yN | m₂ =h [ f(x + y + + 1 m₂ = h [f(xn + ²/² ₁ 4 ₁ + = 7²)
= 0.2 [Y₁-Xn-1)² +2] = 0.2 [((y₁ + 2/2) - (^n + 0.1)-1)=0.2 [((yn+2)-(xn +0.1) −1)²
0
2
3
4
5
=
DATE.
12
+2
m₁ =h [f(xn+h) yn + m₂)] yn + ₁ = y₁= = (m₁ +2m₂ +2m₂ + my)
= 0.2 [((yn + m₂) - (xn +0.2)-1)²
+2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40155426-0be7-42b9-9784-5940dabafc01%2Fdcdfde97-4891-451a-9017-3a406ac64690%2Fcm82fyt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Computation 2:
use the 4th order Runge-Kutta method to solve the differential
(y-x-1)² +2 to find an approximate solution.
dy
equation
_y (0)=1 Find y(1) with h = 0.2. Find %.E.T.
Exact answer :
y = fan x + x + 1 = tan 1 + 1 + 1 = 3.557401 = 3.56
All answer must be correct to 2 decimal places.
|xn|yn|m₁ = h [f(xn₁yN | m₂ =h [ f(x + y + + 1 m₂ = h [f(xn + ²/² ₁ 4 ₁ + = 7²)
= 0.2 [Y₁-Xn-1)² +2] = 0.2 [((y₁ + 2/2) - (^n + 0.1)-1)=0.2 [((yn+2)-(xn +0.1) −1)²
0
2
3
4
5
=
DATE.
12
+2
m₁ =h [f(xn+h) yn + m₂)] yn + ₁ = y₁= = (m₁ +2m₂ +2m₂ + my)
= 0.2 [((yn + m₂) - (xn +0.2)-1)²
+2
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