M- 07. Consider the following first-order ODE: dy _y dt t 0.5t2 from t = 2 to t = 5 with y(2) = 4 (a) Solve with Euler's explicit method using h = 1. (b) Solve with the modified Euler method using h = 1. (c) Solve with the classical third-order Runge-Kutta method using h = 1. The analytical solution of the ODE is y = -+ 3t In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.
M- 07. Consider the following first-order ODE: dy _y dt t 0.5t2 from t = 2 to t = 5 with y(2) = 4 (a) Solve with Euler's explicit method using h = 1. (b) Solve with the modified Euler method using h = 1. (c) Solve with the classical third-order Runge-Kutta method using h = 1. The analytical solution of the ODE is y = -+ 3t In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.
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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Transcribed Image Text:M- 07. Consider the following first-order ODE:
dy _y
dtt
0.5t2
from t = 2 to t = 5 with y(2) = 4
(a) Solve with Euler's explicit method using h = 1.
(b) Solve with the modified Euler method using h = 1.
(c) Solve with the classical third-order Runge-Kutta method using h = 1.
The analytical solution of the ODE is
-+ 3t
In each part, calculate the error between the true solution and the numerical solution at the
y =
points where the numerical solution is determined.
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