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.
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
Problem 1RQ
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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.
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