a- Use Euler’s method to integrate dy/dt = y − t^2 + 1 from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5. b- Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy/dt= y − t^2 + 1 from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5. c- Compare the true percent relative error values ( |Et|%) Note that the exact ( analytical) solution was given in the tables.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a- Use Euler’s method to integrate
dy/dt = y − t^2 + 1
from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5.


b- Employ the classical fourth-order Runge-Kutta (RK) method to integrate
dy/dt= y − t^2 + 1
from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5.

c- Compare the true percent relative error values ( |Et|%)
Note that the exact ( analytical) solution was given in the tables.

 

(c-
Compare the true percent relative error values ( |&|%)
Note that the exact ( analytical) solution was given in the tables.
t
Ytrue
YEuler
|&| (%)
0.0
0.50000
0.50000
0.05
0.57686
0.1
0.65741
0.15
0.74158
0.2
0.82929
t
Ytrue
YFourth-Order RK
|&| (%)
0.0
0.50000
0.50000
---
0.05
0.57686
0.1
0.65741
0.15
0.74158
0.2
0.82929
Transcribed Image Text:(c- Compare the true percent relative error values ( |&|%) Note that the exact ( analytical) solution was given in the tables. t Ytrue YEuler |&| (%) 0.0 0.50000 0.50000 0.05 0.57686 0.1 0.65741 0.15 0.74158 0.2 0.82929 t Ytrue YFourth-Order RK |&| (%) 0.0 0.50000 0.50000 --- 0.05 0.57686 0.1 0.65741 0.15 0.74158 0.2 0.82929
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