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Use Euler’s method to integrate ??/?? = ? − ?^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.

Use Euler’s method to integrate ??/?? = ? − ?^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.

Advanced Engineering Mathematics
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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Use Euler’s method to integrate
??/?? = ? − ?^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.

(a- Use Euler's method to integrate dy = y – t² + 1 dt from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5.
Transcribed Image Text:(a- Use Euler's method to integrate dy = y – t² + 1 dt 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 ( |&|%) 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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