consider the following first-order ODE: dy/dt = y+t³ from t=0 to t=1.5 with y(0) = 1. a). Solve with euler's explicit method using h=0.05. b). Solve with the midpoint method using h=0.05. c). Solve with the classical fourth-order runge-kutta method using h=0.05. The analytical solution of the ODE is y= 7e^t - t³ - 6t-6. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined. Kindly answer a,b, and c.
consider the following first-order ODE: dy/dt = y+t³ from t=0 to t=1.5 with y(0) = 1. a). Solve with euler's explicit method using h=0.05. b). Solve with the midpoint method using h=0.05. c). Solve with the classical fourth-order runge-kutta method using h=0.05. The analytical solution of the ODE is y= 7e^t - t³ - 6t-6. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined. Kindly answer a,b, and c.
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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consider the following first-order ODE:
dy/dt = y+t³ from t=0 to t=1.5 with y(0) = 1.
a). Solve with euler's explicit method using h=0.05.
b). Solve with the midpoint method using h=0.05.
c). Solve with the classical fourth-order runge-kutta method using h=0.05.
The analytical solution of the ODE is
y= 7e^t - t³ - 6t-6. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.
Kindly answer a,b, and c. Thank you
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