ignments: Find a solution for the following equations in two different ways: analytically and numerically, and compare the results estimating the errors. Do 3 steps only for the numerical calculations for: 1/ 1. Euler's method -y' = (y + x)², y(0) = 0, h = 0.1 %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Screenshot at 20...
->
Assignments: Find a solution for the following equations in two different ways: analytically and
numerically, and compare the results estimating the errors. Do 3 steps only for the
numerical calculations for:
Q1/
1.
Euler's method
-y' = (y + x)², y(0) = 0, h = 0.1
%3D
2.
Heun's Method
-y' – xy² = 0, y(0) = 1, h = 0.1
3.
Runge-Kutta (RK4)
y' = 1 + y², y(0) = 0, h = 0.1
%3D
Transcribed Image Text:Screenshot at 20... -> Assignments: Find a solution for the following equations in two different ways: analytically and numerically, and compare the results estimating the errors. Do 3 steps only for the numerical calculations for: Q1/ 1. Euler's method -y' = (y + x)², y(0) = 0, h = 0.1 %3D 2. Heun's Method -y' – xy² = 0, y(0) = 1, h = 0.1 3. Runge-Kutta (RK4) y' = 1 + y², y(0) = 0, h = 0.1 %3D
Screenshot at 20...
->
Assignments:
y' + 5.2y = 19.4 sin 21, y(0) = 0
1.
У — бу %3D 0, у(-1) %3D 4
2.
y" – 6y' + 5y = 29 cos 2t, y(0) = 3.2,
y'(0) = 6.2
3.
y" + 3y' + 2y = 1 if 0 < t < 1 and 0 if t > 1;
y(0) = 0, y'(0) = 0
4.
5.
y" + 2y' + 5y = 25t – 1008(t
y'(0) = 5
т), у(0) %3D — 2,
Transcribed Image Text:Screenshot at 20... -> Assignments: y' + 5.2y = 19.4 sin 21, y(0) = 0 1. У — бу %3D 0, у(-1) %3D 4 2. y" – 6y' + 5y = 29 cos 2t, y(0) = 3.2, y'(0) = 6.2 3. y" + 3y' + 2y = 1 if 0 < t < 1 and 0 if t > 1; y(0) = 0, y'(0) = 0 4. 5. y" + 2y' + 5y = 25t – 1008(t y'(0) = 5 т), у(0) %3D — 2,
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