7. Consider solving the initial value problem dy -= yt? – 1.1y, v(t = 0) = 1, %3D dt from t = 0 to t 1. (a) Find the true solution analytically using separation of variables. Calculate the true values of y(t) for a step size h = 0.5. Use the result to calculate the true relative error in percentage for each of the numerical solutions below. (b) Solve numerically using Euler's method using step size h = 0.5. (c) Solve numerically using fourth order Runge-Kutta method with step size h = 0.5.
7. Consider solving the initial value problem dy -= yt? – 1.1y, v(t = 0) = 1, %3D dt from t = 0 to t 1. (a) Find the true solution analytically using separation of variables. Calculate the true values of y(t) for a step size h = 0.5. Use the result to calculate the true relative error in percentage for each of the numerical solutions below. (b) Solve numerically using Euler's method using step size h = 0.5. (c) Solve numerically using fourth order Runge-Kutta method with step size h = 0.5.
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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